General
This site provides supporting material for the paper Encoding Dependency Pair Techniques and Control Strategies for Maximal Completion by Haruhiko Sato and Sarah Winkler. This paper describes two advancements of SAT-based Knuth- Bendix completion as implemented in Maxcomp. (1) Termination techniques using the dependency pair framework are encoded as satisfiability problems, including dependency graph and reduction pair processors. (2) Instead of relying on pure maximal completion, diㄦent SAT-encoded control strategies are exploited. Experiments show that these developments let Maxcomp improve over other automatic completion tools, and produce novel complete systems.Download
You may want to download the sources and a 64bit executable.Usage
The usage of MaxcompDP is as follows: $ ./maxcompdp -M auto eq_systems/slothrop_cge.trs
The option
-M
allows to specify a strategy for MaxcompDP. Options include
auto
,
lpo
,
kbo
,
mpol
,
dp
,
dg
,
dgk
,
maxcomp
,
red
,
cpred
, and comp
.
The options -N
and -K
allow to set the n and k parameters.
The input file is supposed to be in the
trs format.
Experiments
The following tables summarize results for the test bed comprising 115 equational systems from the distribution of mkbTT, run on a system equipped with an Intel Core i7 with four cores of 2.1GHz each and 7.5 GB of memory. Each ES was given a time limit of 600 seconds,-
comparison with other tools
comparison with other automatic completion tools: the original version of Maxcomp, mkbTT, and KBCV. -
termination strategies
comparison of LPO, DP, DG, DG-2SCC (using Cred+comp+cpred), and the auto setting -
control strategies for DP techniques
comparison of Smaxcomp, Sunoriented, Sred, Scomp, Scpred and Sred+comp+cpred, using DP([LPol,LPO]) -
control strategies for LPO
comparison of Cmaxcomp and Cred+comp+cpred, using LPO
-
k values
comparison of a) fixing k=2 and b) initially choosing k=6 for two iterations
- completions of CGE6 and CGE7
maxcomp | unoriented | red | comp | cpred | full | |
ASK93_1 |
0.03
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.019 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.004 time/update context: 0 Convergent TRS(VAR x)
Completion of ASK93_1
(RULES a(b(x)) → w(a(x))w(a(c(x))) → a(c(x))) |
0.02
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.015 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.009 time/project: 0 time/sat: 0.003 time/update context: 0 Convergent TRS(VAR x)
Completion of ASK93_1
(RULES a(b(x)) → w(a(x))w(a(c(x))) → a(c(x))) |
0.02
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.015 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x)
Completion of ASK93_1
(RULES a(b(x)) → w(a(x))w(a(c(x))) → a(c(x))) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.011 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of ASK93_1
(RULES a(b(x)) → w(a(x))w(a(c(x))) → a(c(x))) |
0.02
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.003 time/update context: 0 Convergent TRS(VAR x)
Completion of ASK93_1
(RULES a(b(x)) → w(a(x))w(a(c(x))) → a(c(x))) |
0.02
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.004 time/update context: 0 Convergent TRS(VAR x)
Completion of ASK93_1
(RULES a(b(x)) → w(a(x))w(a(c(x))) → a(c(x))) |
ASK93_6 |
0.20
Statisticsiterations: 2 equalities (active): 23 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.163 time/normalization: 0.002 time/overlaps: 0.015 time/orientation constraints: 0.065 time/project: 0 time/sat: 0.087 time/update context: 0 Convergent TRS(VAR z)
Completion of ASK93_6
(RULES i(y(z)) → a(z)g(z) → y(b(z))w(e(z)) → h(j(z))e(f(c(z))) → a(b(c(z)))x(w(a(z))) → u(z)o(z) → u(b(c(z)))w(a(b(c(z)))) → h(c(z))x(h(c(z))) → u(b(c(z)))x(w(d(y(z)))) → u(z)x(h(j(y(b(z))))) → x(h(z))d(y(b(c(z)))) → e(y(b(c(z))))x(w(i(z))) → x(w(d(z)))j(f(z)) → z,) |
1.23
Statisticsiterations: 3 equalities (active): 40 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 1.196 time/normalization: 0.002 time/overlaps: 0.009 time/orientation constraints: 0.161 time/project: 0 time/sat: 0.987 time/update context: 0.002 Convergent TRS(VAR z)
Completion of ASK93_6
(RULES i(y(z)) → a(z)g(z) → y(b(z))w(e(z)) → h(j(z))o(z) → x(h(c(z)))x(w(d(z))) → x(w(i(z)))d(y(b(c(z)))) → e(y(b(c(z))))x(h(j(y(b(z))))) → x(h(z))u(z) → x(w(a(z)))a(b(c(z))) → e(f(c(z)))j(f(z)) → z,) |
0.60
Statisticsiterations: 4 equalities (active): 39 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.552 time/normalization: 0.003 time/overlaps: 0.016 time/orientation constraints: 0.324 time/project: 0 time/sat: 0.166 time/update context: 0.001 Convergent TRS(VAR z)
Completion of ASK93_6
(RULES g(z) → y(b(z))w(e(z)) → h(j(z))o(z) → u(b(c(z)))x(w(d(z))) → x(w(i(z)))x(h(c(z))) → u(b(c(z)))w(i(y(b(c(z))))) → h(c(z))e(f(c(z))) → i(y(b(c(z))))x(w(i(y(z)))) → u(z)d(y(b(c(z)))) → e(y(b(c(z))))x(h(j(y(b(z))))) → x(h(z))j(f(z)) → z,a(z) → i(y(z))) |
0.65
Statisticsiterations: 5 equalities (active): 39 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.599 time/normalization: 0.007 time/overlaps: 0.013 time/orientation constraints: 0.329 time/project: 0 time/sat: 0.169 time/update context: 0.004 Convergent TRS(VAR z)
Completion of ASK93_6
(RULES i(y(z)) → a(z)g(z) → y(b(z))w(e(z)) → h(j(z))e(f(c(z))) → a(b(c(z)))x(w(a(z))) → u(z)o(z) → u(b(c(z)))w(d(y(b(c(z))))) → h(j(y(b(c(z)))))w(a(b(c(z)))) → h(c(z))e(y(b(c(z)))) → d(y(b(c(z))))x(w(d(y(z)))) → u(z)x(h(c(z))) → u(b(c(z)))x(h(j(y(b(z))))) → x(h(z))x(w(i(z))) → x(w(d(z)))j(f(z)) → z,) |
0.71
Statisticsiterations: 5 equalities (active): 39 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.671 time/normalization: 0.005 time/overlaps: 0.015 time/orientation constraints: 0.335 time/project: 0 time/sat: 0.254 time/update context: 0.002 Convergent TRS(VAR z)
Completion of ASK93_6
(RULES i(y(z)) → a(z)e(f(c(z))) → a(b(c(z)))x(w(d(z))) → x(w(i(z)))e(g(c(z))) → d(g(c(z)))i(g(z)) → a(b(z))w(e(f(z))) → h(z)x(w(e(g(j(z))))) → x(w(e(z)))o(z) → x(w(a(b(c(z)))))x(h(z)) → x(w(e(g(z))))h(c(z)) → w(a(b(c(z))))u(z) → x(w(a(z)))j(f(z)) → z,h(j(z)) → w(e(z))y(b(z)) → g(z)) |
0.35
Statisticsiterations: 2 equalities (active): 28 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.315 time/normalization: 0.005 time/overlaps: 0.011 time/orientation constraints: 0.119 time/project: 0 time/sat: 0.164 time/update context: 0.001 Convergent TRS(VAR z)
Completion of ASK93_6
(RULES i(y(z)) → a(z)g(z) → y(b(z))w(e(z)) → h(j(z))e(f(c(z))) → a(b(c(z)))x(w(a(z))) → x(w(d(y(z))))o(z) → x(h(c(z)))w(d(y(b(c(z))))) → h(j(y(b(c(z)))))w(a(b(c(z)))) → h(c(z))e(y(b(c(z)))) → d(y(b(c(z))))u(z) → x(w(d(y(z))))x(h(j(y(b(z))))) → x(h(z))x(w(i(z))) → x(w(d(z)))j(f(z)) → z,) |
BD94_collapse |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_collapse
(RULES c → ba → bf(b,x) → bg(x) → x,f(x,b) → x,) |
0.02
Statisticsiterations: 2 equalities (active): 7 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.012 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.007 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_collapse
(RULES a → bc → bg(x) → x,f(x,b) → x,f(b,x) → b) |
0.02
Statisticsiterations: 3 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_collapse
(RULES f(a,x) → af(x,a) → x,b → ac → ag(x) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 7 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_collapse
(RULES a → bc → bg(x) → x,f(x,b) → x,f(b,x) → b) |
0.03
Statisticsiterations: 3 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.021 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_collapse
(RULES a → cf(c,x) → cf(x,c) → x,b → cg(x) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 7 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.003 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_collapse
(RULES a → bc → bg(x) → x,f(x,b) → x,f(b,x) → b) |
BD94_peano |
0.01
Statisticsiterations: 1 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.006 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.003 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y)
Completion of BD94_peano
(RULES +(x,s(y)) → s(+(x,y))+(x,0) → x,*(x,0) → 0*(x,s(y)) → +(*(x,y),x)) |
0.01
Statisticsiterations: 1 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y)
Completion of BD94_peano
(RULES +(x,s(y)) → s(+(x,y))+(x,0) → x,*(x,0) → 0*(x,s(y)) → +(*(x,y),x)) |
0.01
Statisticsiterations: 1 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of BD94_peano
(RULES +(x,s(y)) → s(+(x,y))+(x,0) → x,*(x,0) → 0*(x,s(y)) → +(*(x,y),x)) |
0.01
Statisticsiterations: 1 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y)
Completion of BD94_peano
(RULES +(x,s(y)) → s(+(x,y))+(x,0) → x,*(x,0) → 0*(x,s(y)) → +(*(x,y),x)) |
0.01
Statisticsiterations: 1 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of BD94_peano
(RULES +(x,s(y)) → s(+(x,y))+(x,0) → x,*(x,0) → 0*(x,s(y)) → +(*(x,y),x)) |
0.01
Statisticsiterations: 1 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of BD94_peano
(RULES +(x,s(y)) → s(+(x,y))+(x,0) → x,*(x,0) → 0*(x,s(y)) → +(*(x,y),x)) |
BD94_sqrt |
0.01
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_sqrt
(RULES i(0) → 0+(0,0) → 0sqrt(+(i(x),x)) → 0sqrt(0) → 0) |
0.01
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.004 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_sqrt
(RULES sqrt(0) → 0+(0,0) → 0i(0) → 0sqrt(+(i(x),x)) → 0) |
0.01
Statisticsiterations: 3 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_sqrt
(RULES sqrt(0) → 0+(0,0) → 0i(0) → 0sqrt(+(i(x),x)) → 0) |
0.01
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.006 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.004 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_sqrt
(RULES sqrt(0) → 0+(0,0) → 0i(0) → 0sqrt(+(i(x),x)) → 0) |
0.01
Statisticsiterations: 3 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_sqrt
(RULES sqrt(0) → 0+(0,0) → 0i(0) → 0sqrt(+(i(x),x)) → 0) |
0.01
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.006 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_sqrt
(RULES sqrt(0) → 0+(0,0) → 0i(0) → 0sqrt(+(i(x),x)) → 0) |
BGK94_D08 | ∞ |
18.25
Statisticsiterations: 10 equalities (active): 139 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.015 time/maxk: 17.643 time/normalization: 0.28 time/overlaps: 0.157 time/orientation constraints: 1.311 time/project: 0 time/sat: 11.541 time/update context: 0.293 Convergent TRS(VAR x y z)
Completion of BGK94_D08
(RULES f(a,f(a,f(a,a))) → ef(x,i(x)) → ef(e,x) → x,f(i(x),x) → ei(b) → bf(b,f(a,x)) → f(a,f(a,f(a,f(b,x))))i(f(x,y)) → f(i(y),i(x))i(e) → ei(i(x)) → x,f(x,f(i(x),y)) → y,i(a) → f(a,f(a,a))f(i(x),f(x,y)) → y,f(b,a) → f(a,f(a,f(a,b)))f(a,f(a,f(a,f(a,x)))) → x,f(b,f(b,x)) → x,f(b,b) → ef(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
6.92
Statisticsiterations: 12 equalities (active): 201 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.022 time/maxk: 5.339 time/normalization: 0.743 time/overlaps: 0.406 time/orientation constraints: 2.033 time/project: 0 time/sat: 0.396 time/update context: 0.083 Convergent TRS(VAR x y z)
Completion of BGK94_D08
(RULES f(b,b) → ef(x,i(x)) → ef(i(a),b) → f(b,a)i(b) → bf(a,f(b,a)) → bf(a,f(a,a)) → i(a)f(b,f(a,b)) → i(a)f(a,f(b,f(a,x))) → f(b,x)f(i(a),i(a)) → f(a,a)f(i(a),f(b,x)) → f(b,f(a,x))f(i(a),f(i(a),x)) → f(a,f(a,x))f(i(x),x) → ei(e) → ef(e,x) → x,f(b,f(a,f(a,x))) → f(a,f(a,f(b,x)))f(b,f(a,a)) → f(a,f(a,b))f(a,f(a,f(a,x))) → f(i(a),x)f(b,f(a,f(b,x))) → f(i(a),x)i(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,f(x,f(i(x),y)) → y,f(b,f(b,x)) → x,i(i(x)) → x,f(b,f(i(a),x)) → f(a,f(b,x))f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(b,i(a)) → f(a,b)) |
34.81
Statisticsiterations: 19 equalities (active): 277 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.052 time/maxk: 25.613 time/normalization: 5.356 time/overlaps: 1.031 time/orientation constraints: 4.606 time/project: 0 time/sat: 1.733 time/update context: 1.204 Convergent TRS(VAR x y z)
Completion of BGK94_D08
(RULES f(b,b) → ef(x,i(x)) → ef(a,f(b,a)) → bi(b) → bf(i(x),x) → ef(i(a),b) → f(b,a)f(i(a),i(a)) → f(a,a)f(a,f(b,f(a,x))) → f(b,x)f(i(a),f(b,x)) → f(b,f(a,x))f(a,f(a,a)) → i(a)f(i(a),f(i(a),x)) → f(a,f(a,x))f(b,f(a,f(a,x))) → f(a,f(a,f(b,x)))f(x,f(i(x),y)) → y,f(b,f(b,x)) → x,f(a,f(a,f(a,x))) → f(i(a),x)f(b,f(a,f(b,x))) → f(i(a),x)i(f(x,y)) → f(i(y),i(x))f(b,f(a,a)) → f(a,f(a,b))i(e) → ei(i(x)) → x,f(i(x),f(x,y)) → y,f(e,x) → x,f(b,f(a,b)) → i(a)f(b,f(i(a),x)) → f(a,f(b,x))f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(b,i(a)) → f(a,b)) |
13.23
Statisticsiterations: 11 equalities (active): 144 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.016 time/maxk: 12.748 time/normalization: 0.2 time/overlaps: 0.142 time/orientation constraints: 1.051 time/project: 0 time/sat: 4.559 time/update context: 0.054 Convergent TRS(VAR x y z)
Completion of BGK94_D08
(RULES f(a,f(a,f(a,a))) → ef(x,i(x)) → ef(i(x),x) → ei(b) → bf(b,f(a,x)) → f(a,f(a,f(a,f(b,x))))f(b,a) → f(a,f(a,f(a,b)))i(a) → f(a,f(a,a))i(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,i(e) → ei(i(x)) → x,f(x,f(i(x),y)) → y,f(e,x) → x,f(b,f(b,x)) → x,f(a,f(a,f(a,f(a,x)))) → x,f(b,b) → ef(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
17.43
Statisticsiterations: 9 equalities (active): 143 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 17.026 time/normalization: 0.184 time/overlaps: 0.086 time/orientation constraints: 0.604 time/project: 0 time/sat: 8.503 time/update context: 0.179 Convergent TRS(VAR x y z)
Completion of BGK94_D08
(RULES f(a,f(a,f(a,a))) → ef(x,i(x)) → ef(i(x),x) → ei(b) → bf(b,f(a,x)) → f(a,f(a,f(a,f(b,x))))i(f(x,y)) → f(i(y),i(x))f(b,a) → f(a,f(a,f(a,b)))i(e) → ef(e,x) → x,i(i(x)) → x,f(x,f(i(x),y)) → y,i(a) → f(a,f(a,a))f(i(x),f(x,y)) → y,f(b,f(b,x)) → x,f(a,f(a,f(a,f(a,x)))) → x,f(b,b) → ef(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
BGK94_D10 | ∞ |
18.11
Statisticsiterations: 11 equalities (active): 150 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.019 time/maxk: 17.36 time/normalization: 0.37 time/overlaps: 0.126 time/orientation constraints: 1.9 time/project: 0 time/sat: 9.974 time/update context: 0.345 Convergent TRS(VAR x y z)
Completion of BGK94_D10
(RULES f(b,b) → ef(a,f(a,f(a,f(a,a)))) → ef(x,i(x)) → ef(i(x),x) → ei(b) → bf(b,f(a,x)) → f(a,f(a,f(a,f(a,f(b,x)))))i(f(x,y)) → f(i(y),i(x))f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,f(b,a) → f(a,f(a,f(a,f(a,b))))i(e) → ei(i(x)) → x,i(a) → f(a,f(a,f(a,a)))f(a,f(a,f(a,f(a,f(a,x))))) → x,f(e,x) → x,f(b,f(b,x)) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
9.30
Statisticsiterations: 14 equalities (active): 198 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.035 time/maxk: 7.224 time/normalization: 1 time/overlaps: 0.541 time/orientation constraints: 2.833 time/project: 0 time/sat: 0.468 time/update context: 0.12 Convergent TRS(VAR x y z)
Completion of BGK94_D10
(RULES f(b,b) → ef(x,i(x)) → ef(a,f(b,a)) → bi(b) → bf(i(a),b) → f(b,a)f(a,f(b,f(a,x))) → f(b,x)f(i(x),x) → ef(i(a),f(b,x)) → f(b,f(a,x))f(i(a),f(i(a),i(a))) → f(a,a)f(i(a),f(i(a),f(i(a),x))) → f(a,f(a,x))f(a,f(a,f(a,x))) → f(i(a),f(i(a),x))f(b,f(a,f(a,f(b,x)))) → f(i(a),f(i(a),x))f(b,f(a,f(a,b))) → f(i(a),i(a))f(b,f(a,f(b,x))) → f(i(a),x)i(e) → ef(e,x) → x,i(f(x,y)) → f(i(y),i(x))f(a,f(a,a)) → f(i(a),i(a))i(i(x)) → x,f(i(x),f(x,y)) → y,f(x,f(i(x),y)) → y,f(b,f(b,x)) → x,f(b,f(a,b)) → i(a)f(b,f(i(a),x)) → f(a,f(b,x))f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(b,i(a)) → f(a,b)) |
71.42
Statisticsiterations: 33 equalities (active): 231 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.162 time/maxk: 47.285 time/normalization: 15.61 time/overlaps: 1.899 time/orientation constraints: 7.925 time/project: 0 time/sat: 1.98 time/update context: 2.784 Convergent TRS(VAR x y z)
Completion of BGK94_D10
(RULES f(b,b) → ef(x,i(x)) → ef(a,f(b,a)) → bf(i(a),b) → f(b,a)i(b) → bf(a,f(b,f(a,x))) → f(b,x)f(i(x),x) → ef(i(a),f(b,x)) → f(b,f(a,x))f(i(a),f(i(a),i(a))) → f(a,a)f(b,f(a,f(a,b))) → f(i(a),i(a))f(b,f(a,b)) → i(a)f(i(a),f(i(a),f(i(a),x))) → f(a,f(a,x))f(a,f(a,f(a,x))) → f(i(a),f(i(a),x))f(b,f(a,f(a,f(b,x)))) → f(i(a),f(i(a),x))f(b,f(a,f(b,x))) → f(i(a),x)f(a,f(a,a)) → f(i(a),i(a))i(e) → ef(e,x) → x,i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,f(b,f(b,x)) → x,f(b,f(i(a),x)) → f(a,f(b,x))f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(b,i(a)) → f(a,b)) |
15.47
Statisticsiterations: 10 equalities (active): 117 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 15.168 time/normalization: 0.139 time/overlaps: 0.068 time/orientation constraints: 0.798 time/project: 0 time/sat: 10.656 time/update context: 0.027 Convergent TRS(VAR x y z)
Completion of BGK94_D10
(RULES f(b,b) → ef(x,i(x)) → ef(i(x),x) → ef(a,f(b,a)) → bf(a,f(b,f(a,x))) → f(b,x)i(b) → bf(a,f(a,f(a,x))) → f(b,f(a,f(a,f(b,x))))f(a,f(a,a)) → f(b,f(a,f(a,b)))i(e) → ef(e,x) → x,i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,f(b,f(b,x)) → x,f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,i(a) → f(b,f(a,b))f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
17.81
Statisticsiterations: 10 equalities (active): 140 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.008 time/maxk: 17.293 time/normalization: 0.253 time/overlaps: 0.114 time/orientation constraints: 0.758 time/project: 0 time/sat: 7.323 time/update context: 0.189 Convergent TRS(VAR x y z)
Completion of BGK94_D10
(RULES f(a,f(a,f(a,f(a,a)))) → ef(x,i(x)) → ef(i(x),x) → ei(b) → bf(b,f(a,x)) → f(a,f(a,f(a,f(a,f(b,x)))))i(f(x,y)) → f(i(y),i(x))i(e) → ei(i(x)) → x,f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,i(a) → f(a,f(a,f(a,a)))f(b,a) → f(a,f(a,f(a,f(a,b))))f(b,b) → ef(e,x) → x,f(a,f(a,f(a,f(a,f(a,x))))) → x,f(b,f(b,x)) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
BGK94_D12 | ∞ |
19.15
Statisticsiterations: 12 equalities (active): 140 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.027 time/maxk: 18.136 time/normalization: 0.588 time/overlaps: 0.171 time/orientation constraints: 1.859 time/project: 0 time/sat: 10.323 time/update context: 0.449 Convergent TRS(VAR x y z)
Completion of BGK94_D12
(RULES f(b,b) → ef(a,f(a,f(a,f(a,f(a,a))))) → ef(x,i(x)) → ef(i(x),x) → ei(b) → bf(a,f(a,f(a,f(a,f(a,f(a,x)))))) → x,f(b,a) → f(a,f(a,f(a,f(a,f(a,b)))))f(b,f(a,x)) → f(a,f(a,f(a,f(a,f(a,f(b,x))))))i(e) → ef(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,i(i(x)) → x,i(f(x,y)) → f(i(y),i(x))i(a) → f(a,f(a,f(a,f(a,a))))f(e,x) → x,f(b,f(b,x)) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
15.94
Statisticsiterations: 16 equalities (active): 242 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.078 time/maxk: 9.179 time/normalization: 3.778 time/overlaps: 0.914 time/orientation constraints: 3.564 time/project: 0 time/sat: 0.652 time/update context: 0.14 Convergent TRS(VAR x y z)
Completion of BGK94_D12
(RULES f(b,b) → ef(x,i(x)) → ef(x,f(i(x),y)) → y,f(a,f(b,a)) → bf(i(x),x) → ef(i(a),b) → f(b,a)f(b,f(a,b)) → i(a)i(b) → bf(a,f(a,f(a,a))) → f(i(a),i(a))f(a,f(b,f(a,x))) → f(b,x)f(i(a),f(i(a),i(a))) → f(a,f(a,a))f(i(a),f(b,x)) → f(b,f(a,x))f(i(a),f(i(a),f(i(a),x))) → f(a,f(a,f(a,x)))f(a,f(a,f(a,f(a,x)))) → f(i(a),f(i(a),x))f(b,f(a,f(a,f(a,x)))) → f(a,f(a,f(a,f(b,x))))f(b,f(a,f(a,a))) → f(a,f(a,f(a,b)))f(b,f(a,f(a,f(b,x)))) → f(i(a),f(i(a),x))f(b,f(a,f(a,b))) → f(i(a),i(a))f(b,f(a,f(b,x))) → f(i(a),x)i(f(x,y)) → f(i(y),i(x))i(e) → ei(i(x)) → x,f(b,f(b,x)) → x,f(i(x),f(x,y)) → y,f(e,x) → x,f(b,f(i(a),x)) → f(a,f(b,x))f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(b,i(a)) → f(a,b)) |
143.42
Statisticsiterations: 40 equalities (active): 254 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.241 time/maxk: 86.589 time/normalization: 36.477 time/overlaps: 3.912 time/orientation constraints: 13.847 time/project: 0 time/sat: 6.31 time/update context: 5.755 Convergent TRS(VAR x y z)
Completion of BGK94_D12
(RULES f(b,b) → ef(x,i(x)) → ef(e,x) → x,f(a,f(b,a)) → bi(b) → bf(a,f(b,f(a,x))) → f(b,x)f(i(x),x) → ef(a,f(a,f(a,a))) → f(b,f(a,f(a,b)))f(a,f(a,f(a,b))) → f(b,f(a,f(a,a)))f(a,f(a,f(a,f(b,x)))) → f(b,f(a,f(a,f(a,x))))f(a,f(a,f(a,f(a,x)))) → f(b,f(a,f(a,f(b,x))))i(f(x,y)) → f(i(y),i(x))f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,i(a) → f(b,f(a,b))i(e) → ei(i(x)) → x,f(b,f(b,x)) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
20.13
Statisticsiterations: 10 equalities (active): 147 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.025 time/maxk: 19.423 time/normalization: 0.358 time/overlaps: 0.182 time/orientation constraints: 1.351 time/project: 0 time/sat: 7.992 time/update context: 0.047 Convergent TRS(VAR x y z)
Completion of BGK94_D12
(RULES f(a,f(a,f(a,f(a,f(a,a))))) → ef(x,i(x)) → ef(i(x),x) → ei(b) → bf(b,f(a,x)) → f(a,f(a,f(a,f(a,f(a,f(b,x))))))i(f(x,y)) → f(i(y),i(x))i(e) → ef(e,x) → x,i(i(x)) → x,f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,i(a) → f(a,f(a,f(a,f(a,a))))f(b,a) → f(a,f(a,f(a,f(a,f(a,b)))))f(b,f(b,x)) → x,f(a,f(a,f(a,f(a,f(a,f(a,x)))))) → x,f(b,b) → ef(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
18.28
Statisticsiterations: 9 equalities (active): 144 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.011 time/maxk: 17.497 time/normalization: 0.399 time/overlaps: 0.181 time/orientation constraints: 0.826 time/project: 0 time/sat: 5.702 time/update context: 0.2 Convergent TRS(VAR x y z)
Completion of BGK94_D12
(RULES f(a,f(a,f(a,f(a,f(a,a))))) → ef(x,i(x)) → ef(i(x),x) → ei(b) → bi(e) → ef(b,a) → f(a,f(a,f(a,f(a,f(a,b)))))f(b,f(a,x)) → f(a,f(a,f(a,f(a,f(a,f(b,x))))))i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,f(i(x),f(x,y)) → y,f(x,f(i(x),y)) → y,i(a) → f(a,f(a,f(a,f(a,a))))f(e,x) → x,f(b,f(b,x)) → x,f(a,f(a,f(a,f(a,f(a,f(a,x)))))) → x,f(b,b) → ef(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
BGK94_D16 | ∞ |
51.55
Statisticsiterations: 14 equalities (active): 200 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.174 time/maxk: 45.562 time/normalization: 3.903 time/overlaps: 0.81 time/orientation constraints: 3.148 time/project: 0 time/sat: 18.927 time/update context: 2.892 Convergent TRS(VAR x y z)
Completion of BGK94_D16
(RULES f(a,f(a,f(a,f(a,f(a,f(a,f(a,a))))))) → ef(x,i(x)) → ef(e,x) → x,f(i(x),x) → ei(b) → bf(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,x)))))))) → x,f(b,f(a,x)) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(b,x))))))))i(e) → ef(b,a) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,b)))))))i(f(x,y)) → f(i(y),i(x))f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,i(a) → f(a,f(a,f(a,f(a,f(a,f(a,a))))))f(b,f(b,x)) → x,i(i(x)) → x,f(b,b) → ef(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
67.73
Statisticsiterations: 39 equalities (active): 270 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.329 time/maxk: 39.631 time/normalization: 17.756 time/overlaps: 3.041 time/orientation constraints: 13.399 time/project: 0 time/sat: 2.566 time/update context: 0.535 Convergent TRS(VAR x y z)
Completion of BGK94_D16
(RULES f(b,b) → ef(x,i(x)) → ef(x,f(i(x),y)) → y,f(i(x),x) → ef(b,f(a,b)) → i(a)f(i(a),b) → f(b,a)f(a,f(b,a)) → bi(b) → bf(a,f(b,f(a,x))) → f(b,x)f(i(a),f(b,x)) → f(b,f(a,x))f(b,f(a,f(a,f(a,b)))) → f(i(a),f(i(a),i(a)))f(i(a),f(i(a),f(i(a),i(a)))) → f(a,f(a,f(a,a)))f(i(a),f(i(a),f(i(a),f(i(a),x)))) → f(a,f(a,f(a,f(a,x))))f(a,f(a,f(a,f(a,f(a,x))))) → f(i(a),f(i(a),f(i(a),x)))f(b,f(a,f(a,f(a,f(a,x))))) → f(a,f(a,f(a,f(a,f(b,x)))))f(b,f(a,f(a,f(a,a)))) → f(a,f(a,f(a,f(a,b))))f(a,f(a,f(a,f(a,a)))) → f(i(a),f(i(a),i(a)))f(b,f(a,f(a,f(a,f(b,x))))) → f(i(a),f(i(a),f(i(a),x)))f(b,f(a,f(a,f(b,x)))) → f(i(a),f(i(a),x))i(f(x,y)) → f(i(y),i(x))f(b,f(a,f(a,b))) → f(i(a),i(a))f(b,f(a,f(b,x))) → f(i(a),x)f(i(x),f(x,y)) → y,i(e) → ei(i(x)) → x,f(e,x) → x,f(b,f(b,x)) → x,f(b,f(i(a),x)) → f(a,f(b,x))f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(b,i(a)) → f(a,b)) |
144.65
Statisticsiterations: 38 equalities (active): 225 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.325 time/maxk: 101.672 time/normalization: 29.027 time/overlaps: 3.66 time/orientation constraints: 12.329 time/project: 0 time/sat: 4.345 time/update context: 7.285 Convergent TRS(VAR x y z)
Completion of BGK94_D16
(RULES f(b,b) → ef(x,i(x)) → ef(a,f(b,a)) → bf(i(x),x) → ei(b) → bf(a,f(b,f(a,x))) → f(b,x)f(i(a),b) → f(b,a)f(b,f(a,b)) → i(a)f(i(a),f(b,x)) → f(b,f(a,x))f(i(a),f(i(a),f(i(a),f(i(a),x)))) → f(a,f(a,f(a,f(a,x))))f(i(a),f(i(a),f(i(a),i(a)))) → f(a,f(a,f(a,a)))f(b,f(a,f(a,f(a,a)))) → f(a,f(a,f(a,f(a,b))))f(b,f(a,f(a,f(a,f(a,x))))) → f(a,f(a,f(a,f(a,f(b,x)))))f(b,f(a,f(a,f(a,b)))) → f(i(a),f(i(a),i(a)))f(a,f(a,f(a,f(a,a)))) → f(i(a),f(i(a),i(a)))f(b,f(a,f(a,f(a,f(b,x))))) → f(i(a),f(i(a),f(i(a),x)))f(a,f(a,f(a,f(a,f(a,x))))) → f(i(a),f(i(a),f(i(a),x)))f(b,f(a,f(a,b))) → f(i(a),i(a))f(b,f(a,f(a,f(b,x)))) → f(i(a),f(i(a),x))f(b,f(a,f(b,x))) → f(i(a),x)i(f(x,y)) → f(i(y),i(x))i(e) → ei(i(x)) → x,f(b,f(b,x)) → x,f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,f(e,x) → x,f(b,f(i(a),x)) → f(a,f(b,x))f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(b,i(a)) → f(a,b)) |
55.95
Statisticsiterations: 13 equalities (active): 164 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.03 time/maxk: 54.416 time/normalization: 0.801 time/overlaps: 0.282 time/orientation constraints: 2.248 time/project: 0 time/sat: 33.811 time/update context: 0.066 Convergent TRS(VAR x y z)
Completion of BGK94_D16
(RULES f(a,f(a,f(a,f(a,f(a,f(a,f(a,a))))))) → ef(x,i(x)) → ei(b) → bf(i(x),x) → ef(b,a) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,b)))))))f(b,f(a,x)) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(b,x))))))))i(f(x,y)) → f(i(y),i(x))i(a) → f(a,f(a,f(a,f(a,f(a,f(a,a))))))i(e) → ef(e,x) → x,i(i(x)) → x,f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,f(b,f(b,x)) → x,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,x)))))))) → x,f(b,b) → ef(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
15.54
Statisticsiterations: 9 equalities (active): 123 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 14.825 time/normalization: 0.43 time/overlaps: 0.124 time/orientation constraints: 0.77 time/project: 0 time/sat: 7.859 time/update context: 0.119 Convergent TRS(VAR x y z)
Completion of BGK94_D16
(RULES f(a,f(a,f(a,f(a,f(a,f(a,f(a,a))))))) → ef(x,i(x)) → ef(i(x),x) → ei(b) → bi(a) → f(a,f(a,f(a,f(a,f(a,f(a,a))))))f(b,a) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,b)))))))f(b,f(a,x)) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(b,x))))))))i(f(x,y)) → f(i(y),i(x))i(e) → ef(e,x) → x,i(i(x)) → x,f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,f(b,f(b,x)) → x,f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,x)))))))) → x,f(b,b) → ef(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
BGK94_M08 |
3.31
Statisticsiterations: 6 equalities (active): 82 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.137 time/maxk: 0.522 time/normalization: 0.975 time/overlaps: 0.587 time/orientation constraints: 0.288 time/project: 0 time/sat: 0.155 time/update context: 0.008 Convergent TRS(VAR x y)
Completion of BGK94_M08
(RULES g(x,y) → f6(y)f5(x) → f6(x)f1(x) → f6(x)f6(j(x)) → f6(f6(x))f6(f6(f6(f6(x)))) → f6(x)f8(x) → f6(x)f7(x) → f6(x)f4(x) → f6(x)f3(x) → f6(x)f2(x) → f6(x)) |
∞ |
1.01
Statisticsiterations: 5 equalities (active): 113 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 0.936 time/normalization: 0.01 time/overlaps: 0.023 time/orientation constraints: 0.364 time/project: 0 time/sat: 0.2 time/update context: 0.02 Convergent TRS(VAR x y)
Completion of BGK94_M08
(RULES g(x,y) → f6(y)f6(j(x)) → f6(f6(x))f2(x) → f6(x)f3(x) → f6(x)f5(x) → f6(x)f1(x) → f6(x)f8(x) → f6(x)f6(f6(f6(f6(x)))) → f6(x)f7(x) → f6(x)f4(x) → f6(x)) |
3.11
Statisticsiterations: 6 equalities (active): 102 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.034 time/maxk: 2.745 time/normalization: 0.126 time/overlaps: 0.058 time/orientation constraints: 0.441 time/project: 0 time/sat: 0.428 time/update context: 0.128 Convergent TRS(VAR x y)
Completion of BGK94_M08
(RULES g(x,y) → f1(y)f2(x) → f1(x)f1(j(x)) → f1(f1(x))f3(x) → f1(x)f1(f1(f1(f1(x)))) → f1(x)f4(x) → f1(x)f8(x) → f1(x)f5(x) → f1(x)f6(x) → f1(x)f7(x) → f1(x)) |
2.13
Statisticsiterations: 7 equalities (active): 121 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 2.045 time/normalization: 0.016 time/overlaps: 0.029 time/orientation constraints: 0.49 time/project: 0 time/sat: 0.583 time/update context: 0.02 Convergent TRS(VAR x y)
Completion of BGK94_M08
(RULES g(x,y) → f3(y)f4(x) → f3(x)f1(x) → f3(x)f3(j(x)) → f3(f3(x))f3(f3(f3(f3(x)))) → f3(x)f7(x) → f3(x)f6(x) → f3(x)f2(x) → f3(x)f8(x) → f3(x)f5(x) → f3(x)) |
3.79
Statisticsiterations: 6 equalities (active): 107 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.016 time/maxk: 3.466 time/normalization: 0.123 time/overlaps: 0.07 time/orientation constraints: 0.34 time/project: 0 time/sat: 0.895 time/update context: 0.101 Convergent TRS(VAR x y)
Completion of BGK94_M08
(RULES g(x,y) → f5(y)f1(x) → f5(x)f2(x) → f5(x)f5(j(x)) → f5(f5(x))f3(x) → f5(x)f6(x) → f5(x)f5(f5(f5(f5(x)))) → f5(x)f8(x) → f5(x)f4(x) → f5(x)f7(x) → f5(x)) |
BGK94_M10 |
5.74
Statisticsiterations: 6 equalities (active): 95 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.372 time/maxk: 0.745 time/normalization: 1.449 time/overlaps: 0.654 time/orientation constraints: 0.407 time/project: 0 time/sat: 0.212 time/update context: 0.013 Convergent TRS(VAR x y)
Completion of BGK94_M10
(RULES g(x,y) → f10(y)f3(x) → f10(x)f2(x) → f10(x)f4(x) → f10(x)f5(x) → f10(x)f6(x) → f10(x)f7(x) → f10(x)f8(x) → f10(x)f9(x) → f10(x)f1(x) → f10(x)f10(j(x)) → f10(f10(x))f10(f10(f10(f10(x)))) → f10(x)) |
∞ |
2.45
Statisticsiterations: 9 equalities (active): 136 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.014 time/maxk: 2.335 time/normalization: 0.018 time/overlaps: 0.035 time/orientation constraints: 0.731 time/project: 0 time/sat: 0.629 time/update context: 0.029 Convergent TRS(VAR x y)
Completion of BGK94_M10
(RULES g(x,y) → f8(y)f8(j(x)) → f8(f8(x))f2(x) → f8(x)f3(x) → f8(x)f4(x) → f8(x)f5(x) → f8(x)f6(x) → f8(x)f1(x) → f8(x)f8(f8(f8(f8(x)))) → f8(x)f10(x) → f8(x)f9(x) → f8(x)f7(x) → f8(x)) |
5.42
Statisticsiterations: 7 equalities (active): 121 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.038 time/maxk: 4.786 time/normalization: 0.213 time/overlaps: 0.158 time/orientation constraints: 0.529 time/project: 0 time/sat: 1.146 time/update context: 0.221 Convergent TRS(VAR x y)
Completion of BGK94_M10
(RULES g(x,y) → f2(y)f5(x) → f2(x)f1(x) → f2(x)f2(j(x)) → f2(f2(x))f9(x) → f2(x)f4(x) → f2(x)f2(f2(f2(f2(x)))) → f2(x)f10(x) → f2(x)f7(x) → f2(x)f6(x) → f2(x)f3(x) → f2(x)f8(x) → f2(x)) |
229.88
Statisticsiterations: 10 equalities (active): 144 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 229.729 time/normalization: 0.024 time/overlaps: 0.062 time/orientation constraints: 0.697 time/project: 0 time/sat: 227.119 time/update context: 0.027 Convergent TRS(VAR x y)
Completion of BGK94_M10
(RULES g(x,y) → f6(y)f5(x) → f6(x)f3(x) → f6(x)f2(x) → f6(x)f4(x) → f6(x)f1(x) → f6(x)f6(j(j(j(x)))) → f6(x)f6(j(j(f6(x)))) → f6(x)f6(j(f6(x))) → f6(j(j(x)))f8(x) → f6(x)f10(x) → f6(x)f6(f6(x)) → f6(j(x))f7(x) → f6(x)f9(x) → f6(x)) |
6.14
Statisticsiterations: 6 equalities (active): 107 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.028 time/maxk: 5.738 time/normalization: 0.136 time/overlaps: 0.079 time/orientation constraints: 0.33 time/project: 0 time/sat: 2.447 time/update context: 0.13 Convergent TRS(VAR x y)
Completion of BGK94_M10
(RULES g(x,y) → f2(y)f3(x) → f2(x)f4(x) → f2(x)f1(x) → f2(x)f8(x) → f2(x)f2(j(x)) → f2(f2(x))f2(f2(f2(f2(x)))) → f2(x)f9(x) → f2(x)f7(x) → f2(x)f6(x) → f2(x)f5(x) → f2(x)f10(x) → f2(x)) |
BGK94_M12 |
19.55
Statisticsiterations: 10 equalities (active): 175 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 1.059 time/maxk: 1.854 time/normalization: 6.196 time/overlaps: 2.765 time/orientation constraints: 0.681 time/project: 0 time/sat: 0.837 time/update context: 0.048 Convergent TRS(VAR x y)
Completion of BGK94_M12
(RULES g(x,y) → f10(y)f1(x) → f10(x)f9(x) → f10(x)f8(x) → f10(x)f5(x) → f10(x)f4(x) → f10(x)f3(x) → f10(x)f10(j(x)) → f10(f10(x))f7(x) → f10(x)f6(x) → f10(x)f2(x) → f10(x)f10(f10(f10(f10(x)))) → f10(x)f12(x) → f10(x)f11(x) → f10(x)) |
∞ |
3.04
Statisticsiterations: 6 equalities (active): 113 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.008 time/maxk: 2.939 time/normalization: 0.012 time/overlaps: 0.033 time/orientation constraints: 0.367 time/project: 0 time/sat: 2.121 time/update context: 0.015 Convergent TRS(VAR x y)
Completion of BGK94_M12
(RULES g(x,y) → f2(y)f4(x) → f2(x)f5(x) → f2(x)f8(x) → f2(x)f1(x) → f2(x)f2(j(x)) → f2(f2(x))f3(x) → f2(x)f6(x) → f2(x)f2(f2(f2(f2(x)))) → f2(x)f12(x) → f2(x)f11(x) → f2(x)f10(x) → f2(x)f7(x) → f2(x)f9(x) → f2(x)) |
49.70
Statisticsiterations: 11 equalities (active): 157 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.089 time/maxk: 47.61 time/normalization: 0.626 time/overlaps: 0.646 time/orientation constraints: 2.714 time/project: 0 time/sat: 18.082 time/update context: 1.494 Convergent TRS(VAR x y)
Completion of BGK94_M12
(RULES g(x,y) → f7(y)f6(x) → f7(x)f3(x) → f7(x)f8(x) → f7(x)f2(x) → f7(x)f5(x) → f7(x)f4(x) → f7(x)f1(x) → f7(x)f7(j(x)) → f7(f7(x))f7(f7(f7(f7(x)))) → f7(x)f12(x) → f7(x)f10(x) → f7(x)f9(x) → f7(x)f11(x) → f7(x)) |
4.48
Statisticsiterations: 8 equalities (active): 107 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.012 time/maxk: 4.315 time/normalization: 0.019 time/overlaps: 0.075 time/orientation constraints: 0.541 time/project: 0 time/sat: 2.285 time/update context: 0.019 Convergent TRS(VAR x y)
Completion of BGK94_M12
(RULES g(x,y) → f11(y)f11(j(x)) → f11(f11(x))f2(x) → f11(x)f3(x) → f11(x)f5(x) → f11(x)f6(x) → f11(x)f7(x) → f11(x)f1(x) → f11(x)f10(x) → f11(x)f4(x) → f11(x)f11(f11(f11(f11(x)))) → f11(x)f8(x) → f11(x)f9(x) → f11(x)f12(x) → f11(x)) |
10.24
Statisticsiterations: 7 equalities (active): 127 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.047 time/maxk: 9.407 time/normalization: 0.273 time/overlaps: 0.149 time/orientation constraints: 0.408 time/project: 0 time/sat: 3.312 time/update context: 0.221 Convergent TRS(VAR x y)
Completion of BGK94_M12
(RULES g(x,y) → f2(y)f5(x) → f2(x)f1(x) → f2(x)f4(x) → f2(x)f3(x) → f2(x)f2(j(x)) → f2(f2(x))f2(f2(f2(f2(x)))) → f2(x)f9(x) → f2(x)f7(x) → f2(x)f6(x) → f2(x)f10(x) → f2(x)f12(x) → f2(x)f11(x) → f2(x)f8(x) → f2(x)) |
BGK94_M14 |
17.88
Statisticsiterations: 7 equalities (active): 156 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 1.631 time/maxk: 1.875 time/normalization: 4.701 time/overlaps: 1.81 time/orientation constraints: 0.627 time/project: 0 time/sat: 0.98 time/update context: 0.035 Convergent TRS(VAR x y)
Completion of BGK94_M14
(RULES g(x,y) → f11(y)f1(x) → f11(x)f4(x) → f11(x)f2(x) → f11(x)f3(x) → f11(x)f11(j(x)) → f11(f11(x))f8(x) → f11(x)f5(x) → f11(x)f7(x) → f11(x)f6(x) → f11(x)f11(f11(f11(f11(x)))) → f11(x)f12(x) → f11(x)f14(x) → f11(x)f9(x) → f11(x)f13(x) → f11(x)f10(x) → f11(x)) |
∞ |
10.63
Statisticsiterations: 13 equalities (active): 179 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.028 time/maxk: 10.276 time/normalization: 0.083 time/overlaps: 0.129 time/orientation constraints: 1.817 time/project: 0 time/sat: 5.352 time/update context: 0.085 Convergent TRS(VAR x y)
Completion of BGK94_M14
(RULES g(x,y) → f12(y)f4(x) → f12(x)f11(x) → f12(x)f7(x) → f12(x)f8(x) → f12(x)f1(x) → f12(x)f2(x) → f12(x)f5(x) → f12(x)f12(j(x)) → f12(f12(x))f3(x) → f12(x)f12(f12(f12(f12(x)))) → f12(x)f13(x) → f12(x)f6(x) → f12(x)f10(x) → f12(x)f9(x) → f12(x)f14(x) → f12(x)) |
26.37
Statisticsiterations: 9 equalities (active): 168 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.261 time/maxk: 23.677 time/normalization: 0.888 time/overlaps: 0.428 time/orientation constraints: 1.229 time/project: 0 time/sat: 11.988 time/update context: 0.653 Convergent TRS(VAR x y)
Completion of BGK94_M14
(RULES g(x,y) → f5(y)f3(x) → f5(x)f4(x) → f5(x)f1(x) → f5(x)f10(x) → f5(x)f5(j(x)) → f5(f5(x))f2(x) → f5(x)f9(x) → f5(x)f5(f5(f5(f5(x)))) → f5(x)f11(x) → f5(x)f13(x) → f5(x)f12(x) → f5(x)f14(x) → f5(x)f8(x) → f5(x)f7(x) → f5(x)f6(x) → f5(x)) |
17.40
Statisticsiterations: 11 equalities (active): 179 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.025 time/maxk: 17.166 time/normalization: 0.034 time/overlaps: 0.088 time/orientation constraints: 0.995 time/project: 0 time/sat: 11.37 time/update context: 0.05 Convergent TRS(VAR x y)
Completion of BGK94_M14
(RULES g(x,y) → f1(y)f2(x) → f1(x)f13(x) → f1(x)f4(x) → f1(x)f3(x) → f1(x)f11(x) → f1(x)f10(x) → f1(x)f5(x) → f1(x)f1(f1(x)) → f1(j(x))f1(j(j(j(x)))) → f1(x)f1(j(j(f1(x)))) → f1(x)f1(j(f1(x))) → f1(j(j(x)))f6(x) → f1(x)f9(x) → f1(x)f12(x) → f1(x)f7(x) → f1(x)f8(x) → f1(x)f14(x) → f1(x)) |
47.07
Statisticsiterations: 12 equalities (active): 233 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.091 time/maxk: 45.651 time/normalization: 0.425 time/overlaps: 0.368 time/orientation constraints: 1.338 time/project: 0 time/sat: 22.897 time/update context: 0.6 Convergent TRS(VAR x y)
Completion of BGK94_M14
(RULES g(x,y) → f13(y)f1(x) → f13(x)f4(x) → f13(x)f6(x) → f13(x)f11(x) → f13(x)f3(x) → f13(x)f9(x) → f13(x)f8(x) → f13(x)f2(x) → f13(x)f5(x) → f13(x)f13(j(j(j(x)))) → f13(x)f13(j(j(f13(x)))) → f13(x)f7(x) → f13(x)f10(x) → f13(x)f13(j(f13(x))) → f13(j(j(x)))f13(f13(x)) → f13(j(x))f12(x) → f13(x)f14(x) → f13(x)) |
BH96_fac8_theory |
0.09
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.073 time/normalization: 0 time/overlaps: 0.004 time/orientation constraints: 0.044 time/project: 0 time/sat: 0.021 time/update context: 0 Convergent TRS(VAR x)
Completion of BH96_fac8_theory
(RULES *(s(x),fac(x)) → fac(s(x))s(0) → fac(0)*(+(x,s(y)),fac(+(x,y))) → fac(+(x,s(y)))*(fac(0),fac(0)) → fac(fac(0))+(x,0) → x,s(+(x,y)) → +(x,s(y))*(x,0) → 0*(x,s(y)) → +(*(x,y),x)) |
0.07
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.064 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.031 time/project: 0 time/sat: 0.024 time/update context: 0 Convergent TRS(VAR x)
Completion of BH96_fac8_theory
(RULES +(x,s(y)) → s(+(x,y))+(x,0) → x,*(x,0) → 0*(x,s(y)) → +(*(x,y),x)fac(0) → s(0)fac(s(x)) → *(s(x),fac(x))) |
0.07
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.058 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.039 time/project: 0 time/sat: 0.011 time/update context: 0 Convergent TRS(VAR x)
Completion of BH96_fac8_theory
(RULES *(s(x),fac(x)) → fac(s(x))+(x,s(y)) → s(+(x,y))*(s(0),s(0)) → fac(s(0))+(x,0) → x,*(x,0) → 0*(x,s(y)) → +(*(x,y),x)fac(0) → s(0)) |
0.07
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.051 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.033 time/project: 0 time/sat: 0.01 time/update context: 0 Convergent TRS(VAR x)
Completion of BH96_fac8_theory
(RULES *(s(x),fac(x)) → fac(s(x))+(x,s(y)) → s(+(x,y))*(s(0),s(0)) → fac(s(0))+(x,0) → x,*(x,0) → 0*(x,s(y)) → +(*(x,y),x)fac(0) → s(0)) |
0.10
Statisticsiterations: 3 equalities (active): 15 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.089 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.06 time/project: 0 time/sat: 0.016 time/update context: 0 Convergent TRS(VAR x)
Completion of BH96_fac8_theory
(RULES *(s(x),fac(x)) → fac(s(x))s(0) → fac(0)+(*(x,y),x) → *(x,s(y))*(+(x,s(y)),fac(+(x,y))) → fac(+(x,s(y)))+(*(y,y),s(y)) → s(*(y,s(y)))*(fac(0),fac(0)) → fac(fac(0))*(*(s(y),s(y)),fac(+(*(s(y),y),y))) → fac(*(s(y),s(y)))*(0,s(y)) → *(0,y)+(x,0) → x,s(+(x,y)) → +(x,s(y))*(x,0) → 0) |
0.10
Statisticsiterations: 3 equalities (active): 15 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.081 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.054 time/project: 0 time/sat: 0.014 time/update context: 0 Convergent TRS(VAR x)
Completion of BH96_fac8_theory
(RULES *(s(x),fac(x)) → fac(s(x))s(0) → fac(0)+(*(x,y),x) → *(x,s(y))+(x,s(y)) → s(+(x,y))*(fac(0),fac(0)) → fac(fac(0))s(+(*(s(y),y),y)) → *(s(y),s(y))*(*(s(y),s(y)),fac(+(*(s(y),y),y))) → fac(*(s(y),s(y)))*(0,s(y)) → *(0,y)+(x,0) → x,*(x,0) → 0) |
Chr89_A2 | ∞ |
20.83
Statisticsiterations: 12 equalities (active): 167 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.01 time/maxk: 20.459 time/normalization: 0.15 time/overlaps: 0.101 time/orientation constraints: 1.082 time/project: 0 time/sat: 16.849 time/update context: 0.144 Convergent TRS(VAR x y z)
Completion of Chr89_A2
(RULES f(x,i2(x)) → a2f(i2(x),a2) → i2(x)i2(f(x,y)) → f(i2(y),i2(x))i1(x) → f(i2(x),a1)f(i2(x),f(x,y)) → y,i2(i2(x)) → f(x,a2)i2(a1) → a2i2(a2) → a2f(x,f(i2(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(a1,x) → x,f(a2,x) → x,) |
252.24
Statisticsiterations: 33 equalities (active): 571 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.578 time/maxk: 115.473 time/normalization: 65.894 time/overlaps: 10.435 time/orientation constraints: 28.603 time/project: 0 time/sat: 15.958 time/update context: 1.291 Convergent TRS(VAR x y z)
Completion of Chr89_A2
(RULES f(x,i1(x)) → a1f(i1(x),a1) → i1(x)i2(x) → f(i1(x),a2)i1(f(x,y)) → f(i1(y),i1(x))f(i1(x),f(x,y)) → y,i1(i1(x)) → f(x,a1)i1(a1) → a1i1(a2) → a1f(x,f(i1(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(a1,x) → x,f(a2,x) → x,) |
19.77
Statisticsiterations: 13 equalities (active): 205 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.059 time/maxk: 15.726 time/normalization: 1.928 time/overlaps: 0.696 time/orientation constraints: 3.061 time/project: 0 time/sat: 0.594 time/update context: 1.177 Convergent TRS(VAR x y z)
Completion of Chr89_A2
(RULES f(x,i2(x)) → i2(a1)f(x,i1(x)) → a1a2 → i2(a1)f(x,i2(a1)) → i2(i2(x))f(x,a1) → i1(i2(x))f(i1(x),y) → f(i2(x),y)i1(i1(x)) → i1(i2(x))i2(i1(x)) → i2(i2(x))i1(i2(i2(x))) → i1(x)i1(f(x,y)) → f(i2(y),i1(x))i2(f(x,y)) → f(i2(y),i2(x))i2(i2(i2(x))) → i2(x)f(i2(x),f(x,y)) → y,f(i2(i2(x)),y) → f(x,y)i1(i2(a1)) → a1i2(i2(a1)) → i2(a1)f(i2(a1),x) → x,i1(a1) → a1f(x,f(i2(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(a1,x) → x,) |
62.85
Statisticsiterations: 16 equalities (active): 251 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.04 time/maxk: 61.321 time/normalization: 0.565 time/overlaps: 0.433 time/orientation constraints: 2.679 time/project: 0 time/sat: 10.904 time/update context: 0.162 Convergent TRS(VAR x y z)
Completion of Chr89_A2
(RULES f(x,i1(x)) → a1f(i1(x),a1) → i1(x)i1(f(x,y)) → f(i1(y),i1(x))i2(x) → f(i1(x),a2)f(i1(x),f(x,y)) → y,i1(i1(x)) → f(x,a1)i1(a1) → a1i1(a2) → a1f(x,f(i1(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(a1,x) → x,f(a2,x) → x,) |
38.76
Statisticsiterations: 13 equalities (active): 215 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.019 time/maxk: 37.486 time/normalization: 0.502 time/overlaps: 0.393 time/orientation constraints: 1.631 time/project: 0 time/sat: 1.305 time/update context: 0.495 Convergent TRS(VAR x y z)
Completion of Chr89_A2
(RULES f(x,i1(x)) → a1f(i1(x),a1) → i1(x)f(i1(x),f(x,y)) → y,i1(f(x,y)) → f(i1(y),i1(x))i2(x) → f(i1(x),a2)i1(i1(x)) → f(x,a1)i1(a1) → a1i1(a2) → a1f(x,f(i1(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(a1,x) → x,f(a2,x) → x,) |
Chr89_A3 | ∞ | ∞ |
372.89
Statisticsiterations: 45 equalities (active): 775 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.901 time/maxk: 305.19 time/normalization: 27.481 time/overlaps: 12.773 time/orientation constraints: 32.452 time/project: 0 time/sat: 31.491 time/update context: 3.946 Convergent TRS(VAR x y z)
Completion of Chr89_A3
(RULES f(x,i3(x)) → a3f(i3(x),a3) → i3(x)i3(i3(x)) → f(x,a3)i3(f(x,y)) → f(i3(y),i3(x))i1(x) → f(i3(x),a1)i2(x) → f(i3(x),a2)f(i3(x),f(x,y)) → y,i3(a2) → a3i3(a1) → a3i3(a3) → a3f(x,f(i3(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(a1,x) → x,f(a2,x) → x,f(a3,x) → x,) |
241.69
Statisticsiterations: 23 equalities (active): 413 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.273 time/maxk: 218.414 time/normalization: 12.95 time/overlaps: 2.468 time/orientation constraints: 7.978 time/project: 0 time/sat: 22.282 time/update context: 11.49 Convergent TRS(VAR x y z)
Completion of Chr89_A3
(RULES f(x,i3(x)) → a3f(i3(x),a3) → i3(x)i1(x) → f(i3(x),a1)i3(f(x,y)) → f(i3(y),i3(x))i2(x) → f(i3(x),a2)f(i3(x),f(x,y)) → y,i3(i3(x)) → f(x,a3)i3(a1) → a3i3(a2) → a3i3(a3) → a3f(x,f(i3(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(a1,x) → x,f(a2,x) → x,f(a3,x) → x,) |
304.14
Statisticsiterations: 24 equalities (active): 383 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.11 time/maxk: 300.598 time/normalization: 1.041 time/overlaps: 1.102 time/orientation constraints: 7.114 time/project: 0 time/sat: 43.423 time/update context: 0.643 Convergent TRS(VAR x y z)
Completion of Chr89_A3
(RULES f(x,i1(x)) → a1f(i1(x),a1) → i1(x)i2(x) → f(i1(x),a2)i1(f(x,y)) → f(i1(y),i1(x))f(i1(x),f(x,y)) → y,i3(x) → f(i1(x),a3)i1(i1(x)) → f(x,a1)i1(a1) → a1i1(a2) → a1i1(a3) → a1f(x,f(i1(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(a1,x) → x,f(a2,x) → x,f(a3,x) → x,) |
∞ |
KK99_linear_assoc |
0.02
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.012 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of KK99_linear_assoc
(RULES +(+(x,y),z) → +(x,+(y,z))f(+(x,y)) → +(f(x),f(y))) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of KK99_linear_assoc
(RULES +(+(x,y),z) → +(x,+(y,z))f(+(x,y)) → +(f(x),f(y))) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.006 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of KK99_linear_assoc
(RULES +(x,+(y,z)) → +(+(x,y),z)f(+(x,y)) → +(f(x),f(y))) |
0.04
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.033 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.025 time/project: 0 time/sat: 0.003 time/update context: 0 Convergent TRS(VAR x y z)
Completion of KK99_linear_assoc
(RULES +(x,+(y,z)) → +(+(x,y),z)f(+(x,y)) → +(f(x),f(y))) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.008 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of KK99_linear_assoc
(RULES +(x,+(y,z)) → +(+(x,y),z)f(+(x,y)) → +(f(x),f(y))) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.006 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of KK99_linear_assoc
(RULES +(x,+(y,z)) → +(+(x,y),z)f(+(x,y)) → +(f(x),f(y))) |
LS06_CGE4 | ∞ |
9.77
Statisticsiterations: 9 equalities (active): 149 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.086 time/maxk: 7.537 time/normalization: 0.897 time/overlaps: 0.565 time/orientation constraints: 2.181 time/project: 0 time/sat: 2.934 time/update context: 0.351 Convergent TRS(VAR x y z)
Completion of LS06_CGE4
(RULES *(g(x),k(y)) → *(k(y),g(x))*(h(x),k(y)) → *(k(y),h(x))*(f(x),k(y)) → *(k(y),f(x))*(f(x),g(y)) → *(g(y),f(x))*(k(x),k(y)) → k(*(x,y))*(h(x),h(y)) → h(*(x,y))*(g(x),g(y)) → g(*(x,y))*(f(x),f(y)) → f(*(x,y))*(h(x),*(k(y),z)) → *(k(y),*(h(x),z))*(g(x),*(k(y),z)) → *(k(y),*(g(x),z))*(f(x),*(k(y),z)) → *(k(y),*(f(x),z))*(g(x),*(g(y),z)) → *(g(*(x,y)),z)*(h(x),*(h(y),z)) → *(h(*(x,y)),z)*(k(x),*(k(y),z)) → *(k(*(x,y)),z)i(k(x)) → k(i(x))i(h(x)) → h(i(x))i(g(x)) → g(i(x))i(f(x)) → f(i(x))*(f(x),*(g(y),z)) → *(g(y),*(f(x),z))*(f(x),*(f(y),z)) → *(f(*(x,y)),z)*(h(x),*(g(y),z)) → *(g(y),*(h(x),z))f(one) → one*(x,*(i(x),y)) → y,i(*(x,y)) → *(i(y),i(x))g(one) → oneh(one) → onek(one) → onei(one) → onei(i(x)) → x,*(x,one) → x,*(x,i(x)) → one*(i(x),*(x,y)) → y,*(h(x),*(f(y),z)) → *(f(y),*(h(x),z))*(one,x) → x,*(i(x),x) → one*(*(x,y),z) → *(x,*(y,z))*(h(x),f(y)) → *(f(y),h(x))*(h(x),g(y)) → *(g(y),h(x))) |
∞ | ∞ |
78.83
Statisticsiterations: 8 equalities (active): 126 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.085 time/maxk: 76.822 time/normalization: 0.679 time/overlaps: 0.653 time/orientation constraints: 0.959 time/project: 0 time/sat: 68.264 time/update context: 0.026 Convergent TRS(VAR x y z)
Completion of LS06_CGE4
(RULES *(h(x),k(y)) → *(k(y),h(x))*(f(x),g(y)) → *(g(y),f(x))*(k(x),k(y)) → k(*(x,y))*(h(x),h(y)) → h(*(x,y))*(g(x),g(y)) → g(*(x,y))*(f(x),f(y)) → f(*(x,y))*(h(x),*(k(y),z)) → *(k(y),*(h(x),z))*(f(x),*(g(y),z)) → *(g(y),*(f(x),z))*(f(x),*(f(y),z)) → *(f(*(x,y)),z)*(g(x),*(g(y),z)) → *(g(*(x,y)),z)*(h(x),*(h(y),z)) → *(h(*(x,y)),z)*(k(x),*(k(y),z)) → *(k(*(x,y)),z)i(k(x)) → k(i(x))i(h(x)) → h(i(x))i(g(x)) → g(i(x))i(f(x)) → f(i(x))*(x,*(i(x),y)) → y,i(*(x,y)) → *(i(y),i(x))f(one) → oneg(one) → onek(one) → oneh(one) → onei(one) → onei(i(x)) → x,*(x,one) → x,*(x,i(x)) → one*(i(x),*(x,y)) → y,*(k(x),*(f(y),z)) → *(f(y),*(k(x),z))*(h(x),*(f(y),z)) → *(f(y),*(h(x),z))*(h(x),*(g(y),z)) → *(g(y),*(h(x),z))*(k(x),*(g(y),z)) → *(g(y),*(k(x),z))*(one,x) → x,*(i(x),x) → one*(*(x,y),z) → *(x,*(y,z))*(h(x),f(y)) → *(f(y),h(x))*(h(x),g(y)) → *(g(y),h(x))*(k(x),f(y)) → *(f(y),k(x))*(k(x),g(y)) → *(g(y),k(x))) |
94.35
Statisticsiterations: 10 equalities (active): 147 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.086 time/maxk: 91.989 time/normalization: 0.819 time/overlaps: 0.761 time/orientation constraints: 1.277 time/project: 0 time/sat: 77.772 time/update context: 0.358 Convergent TRS(VAR x y z)
Completion of LS06_CGE4
(RULES *(h(x),k(y)) → *(k(y),h(x))*(k(x),k(y)) → k(*(x,y))*(h(x),h(y)) → h(*(x,y))*(g(x),g(y)) → g(*(x,y))*(f(x),f(y)) → f(*(x,y))*(h(x),*(k(y),z)) → *(k(y),*(h(x),z))*(f(x),*(f(y),z)) → *(f(*(x,y)),z)*(g(x),*(g(y),z)) → *(g(*(x,y)),z)*(h(x),*(h(y),z)) → *(h(*(x,y)),z)*(k(x),*(k(y),z)) → *(k(*(x,y)),z)i(k(x)) → k(i(x))i(g(x)) → g(i(x))i(f(x)) → f(i(x))i(h(x)) → h(i(x))*(x,*(i(x),y)) → y,i(*(x,y)) → *(i(y),i(x))g(one) → oneh(one) → onek(one) → onef(one) → onei(one) → onei(i(x)) → x,*(x,one) → x,*(x,i(x)) → one*(i(x),*(x,y)) → y,*(k(x),*(g(y),z)) → *(g(y),*(k(x),z))*(g(x),*(f(y),z)) → *(f(y),*(g(x),z))*(h(x),*(f(y),z)) → *(f(y),*(h(x),z))*(h(x),*(g(y),z)) → *(g(y),*(h(x),z))*(k(x),*(f(y),z)) → *(f(y),*(k(x),z))*(one,x) → x,*(i(x),x) → one*(*(x,y),z) → *(x,*(y,z))*(g(x),f(y)) → *(f(y),g(x))*(h(x),f(y)) → *(f(y),h(x))*(h(x),g(y)) → *(g(y),h(x))*(k(x),f(y)) → *(f(y),k(x))*(k(x),g(y)) → *(g(y),k(x))) |
LS06_CGE5 | ∞ |
15.89
Statisticsiterations: 12 equalities (active): 196 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.086 time/maxk: 12.687 time/normalization: 1.216 time/overlaps: 0.714 time/orientation constraints: 2.423 time/project: 0 time/sat: 6.69 time/update context: 0.577 Convergent TRS(VAR x y z)
Completion of LS06_CGE5
(RULES *(g(x),k(y)) → *(k(y),g(x))*(h(x),k(y)) → *(k(y),h(x))*(f(x),k(y)) → *(k(y),f(x))*(g(x),h(y)) → *(h(y),g(x))*(f(x),h(y)) → *(h(y),f(x))*(f(x),g(y)) → *(g(y),f(x))*(j(x),j(y)) → j(*(x,y))*(k(x),k(y)) → k(*(x,y))*(h(x),h(y)) → h(*(x,y))*(g(x),g(y)) → g(*(x,y))*(f(x),f(y)) → f(*(x,y))*(f(x),*(k(y),z)) → *(k(y),*(f(x),z))*(h(x),*(k(y),z)) → *(k(y),*(h(x),z))*(f(x),*(h(y),z)) → *(h(y),*(f(x),z))*(g(x),*(h(y),z)) → *(h(y),*(g(x),z))*(f(x),*(f(y),z)) → *(f(*(x,y)),z)*(g(x),*(g(y),z)) → *(g(*(x,y)),z)*(h(x),*(h(y),z)) → *(h(*(x,y)),z)*(k(x),*(k(y),z)) → *(k(*(x,y)),z)*(j(x),*(j(y),z)) → *(j(*(x,y)),z)i(j(x)) → j(i(x))i(h(x)) → h(i(x))i(g(x)) → g(i(x))i(f(x)) → f(i(x))i(k(x)) → k(i(x))*(g(x),*(k(y),z)) → *(k(y),*(g(x),z))*(f(x),*(g(y),z)) → *(g(y),*(f(x),z))i(*(x,y)) → *(i(y),i(x))k(one) → onei(one) → onei(i(x)) → x,g(one) → onej(one) → oneh(one) → onef(one) → one*(x,one) → x,*(x,i(x)) → one*(x,*(i(x),y)) → y,*(i(x),*(x,y)) → y,*(j(x),*(k(y),z)) → *(k(y),*(j(x),z))*(j(x),*(h(y),z)) → *(h(y),*(j(x),z))*(j(x),*(g(y),z)) → *(g(y),*(j(x),z))*(j(x),*(f(y),z)) → *(f(y),*(j(x),z))*(one,x) → x,*(i(x),x) → one*(*(x,y),z) → *(x,*(y,z))*(j(x),f(y)) → *(f(y),j(x))*(j(x),g(y)) → *(g(y),j(x))*(j(x),h(y)) → *(h(y),j(x))*(j(x),k(y)) → *(k(y),j(x))) |
∞ |
302.74
Statisticsiterations: 20 equalities (active): 350 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 9.233 time/maxk: 159.68 time/normalization: 68.163 time/overlaps: 19.709 time/orientation constraints: 27.35 time/project: 0 time/sat: 5.799 time/update context: 40.321 Convergent TRS(VAR x y z)
Completion of LS06_CGE5
(RULES *(f(x),j(y)) → *(j(y),f(x))*(g(x),k(y)) → *(k(y),g(x))*(h(x),k(y)) → *(k(y),h(x))*(f(x),k(y)) → *(k(y),f(x))*(g(x),h(y)) → *(h(y),g(x))*(f(x),h(y)) → *(h(y),f(x))*(f(x),g(y)) → *(g(y),f(x))*(j(x),j(y)) → j(*(x,y))*(k(x),k(y)) → k(*(x,y))*(h(x),h(y)) → h(*(x,y))*(g(x),g(y)) → g(*(x,y))*(f(x),f(y)) → f(*(x,y))*(g(x),*(h(y),z)) → *(h(y),*(g(x),z))*(f(x),*(h(y),z)) → *(h(y),*(f(x),z))*(f(x),*(g(y),z)) → *(g(y),*(f(x),z))*(f(x),*(k(y),z)) → *(k(y),*(f(x),z))*(h(x),*(k(y),z)) → *(k(y),*(h(x),z))*(g(x),*(k(y),z)) → *(k(y),*(g(x),z))*(f(x),*(j(y),z)) → *(j(y),*(f(x),z))*(f(x),*(f(y),z)) → *(f(*(x,y)),z)*(g(x),*(g(y),z)) → *(g(*(x,y)),z)*(h(x),*(h(y),z)) → *(h(*(x,y)),z)*(k(x),*(k(y),z)) → *(k(*(x,y)),z)*(j(x),*(j(y),z)) → *(j(*(x,y)),z)i(j(x)) → j(i(x))i(h(x)) → h(i(x))i(g(x)) → g(i(x))i(f(x)) → f(i(x))i(k(x)) → k(i(x))i(*(x,y)) → *(i(y),i(x))f(one) → oneg(one) → oneh(one) → onek(one) → onej(one) → onei(one) → onei(i(x)) → x,*(x,one) → x,*(x,i(x)) → one*(x,*(i(x),y)) → y,*(i(x),*(x,y)) → y,*(j(x),*(k(y),z)) → *(k(y),*(j(x),z))*(j(x),*(h(y),z)) → *(h(y),*(j(x),z))*(j(x),*(g(y),z)) → *(g(y),*(j(x),z))*(one,x) → x,*(i(x),x) → one*(*(x,y),z) → *(x,*(y,z))*(j(x),g(y)) → *(g(y),j(x))*(j(x),h(y)) → *(h(y),j(x))*(j(x),k(y)) → *(k(y),j(x))) |
273.47
Statisticsiterations: 9 equalities (active): 159 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.194 time/maxk: 269.361 time/normalization: 1.398 time/overlaps: 1.232 time/orientation constraints: 2.093 time/project: 0 time/sat: 247.499 time/update context: 0.054 Convergent TRS(VAR x y z)
Completion of LS06_CGE5
(RULES *(k(x),j(y)) → *(j(y),k(x))*(g(x),j(y)) → *(j(y),g(x))*(g(x),h(y)) → *(h(y),g(x))*(j(x),j(y)) → j(*(x,y))*(k(x),k(y)) → k(*(x,y))*(h(x),h(y)) → h(*(x,y))*(g(x),g(y)) → g(*(x,y))*(f(x),f(y)) → f(*(x,y))*(g(x),*(h(y),z)) → *(h(y),*(g(x),z))*(g(x),*(j(y),z)) → *(j(y),*(g(x),z))*(f(x),*(f(y),z)) → *(f(*(x,y)),z)*(k(x),*(j(y),z)) → *(j(y),*(k(x),z))*(g(x),*(g(y),z)) → *(g(*(x,y)),z)*(h(x),*(h(y),z)) → *(h(*(x,y)),z)*(k(x),*(k(y),z)) → *(k(*(x,y)),z)*(j(x),*(j(y),z)) → *(j(*(x,y)),z)i(f(x)) → f(i(x))i(j(x)) → j(i(x))i(k(x)) → k(i(x))i(h(x)) → h(i(x))i(g(x)) → g(i(x))*(x,*(i(x),y)) → y,i(*(x,y)) → *(i(y),i(x))f(one) → oneg(one) → oneh(one) → onek(one) → onej(one) → onei(one) → onei(i(x)) → x,*(x,one) → x,*(x,i(x)) → one*(i(x),*(x,y)) → y,*(j(x),*(h(y),z)) → *(h(y),*(j(x),z))*(j(x),*(f(y),z)) → *(f(y),*(j(x),z))*(h(x),*(f(y),z)) → *(f(y),*(h(x),z))*(g(x),*(f(y),z)) → *(f(y),*(g(x),z))*(k(x),*(h(y),z)) → *(h(y),*(k(x),z))*(k(x),*(f(y),z)) → *(f(y),*(k(x),z))*(k(x),*(g(y),z)) → *(g(y),*(k(x),z))*(one,x) → x,*(i(x),x) → one*(*(x,y),z) → *(x,*(y,z))*(g(x),f(y)) → *(f(y),g(x))*(h(x),f(y)) → *(f(y),h(x))*(k(x),f(y)) → *(f(y),k(x))*(k(x),h(y)) → *(h(y),k(x))*(k(x),g(y)) → *(g(y),k(x))*(j(x),f(y)) → *(f(y),j(x))*(j(x),h(y)) → *(h(y),j(x))) |
79.49
Statisticsiterations: 8 equalities (active): 139 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.083 time/maxk: 77.239 time/normalization: 0.743 time/overlaps: 0.816 time/orientation constraints: 1.076 time/project: 0 time/sat: 67.879 time/update context: 0.263 Convergent TRS(VAR x y z)
Completion of LS06_CGE5
(RULES *(k(x),j(y)) → *(j(y),k(x))*(h(x),j(y)) → *(j(y),h(x))*(g(x),j(y)) → *(j(y),g(x))*(f(x),j(y)) → *(j(y),f(x))*(g(x),h(y)) → *(h(y),g(x))*(f(x),h(y)) → *(h(y),f(x))*(j(x),j(y)) → j(*(x,y))*(k(x),k(y)) → k(*(x,y))*(h(x),h(y)) → h(*(x,y))*(g(x),g(y)) → g(*(x,y))*(f(x),f(y)) → f(*(x,y))*(g(x),*(h(y),z)) → *(h(y),*(g(x),z))*(f(x),*(h(y),z)) → *(h(y),*(f(x),z))*(f(x),*(j(y),z)) → *(j(y),*(f(x),z))*(g(x),*(j(y),z)) → *(j(y),*(g(x),z))*(h(x),*(j(y),z)) → *(j(y),*(h(x),z))*(k(x),*(j(y),z)) → *(j(y),*(k(x),z))*(f(x),*(f(y),z)) → *(f(*(x,y)),z)*(g(x),*(g(y),z)) → *(g(*(x,y)),z)*(h(x),*(h(y),z)) → *(h(*(x,y)),z)*(k(x),*(k(y),z)) → *(k(*(x,y)),z)*(j(x),*(j(y),z)) → *(j(*(x,y)),z)i(k(x)) → k(i(x))i(h(x)) → h(i(x))i(g(x)) → g(i(x))i(f(x)) → f(i(x))i(j(x)) → j(i(x))i(*(x,y)) → *(i(y),i(x))*(x,*(i(x),y)) → y,f(one) → oneg(one) → oneh(one) → onej(one) → onek(one) → onei(one) → onei(i(x)) → x,*(x,one) → x,*(x,i(x)) → one*(i(x),*(x,y)) → y,*(k(x),*(g(y),z)) → *(g(y),*(k(x),z))*(k(x),*(h(y),z)) → *(h(y),*(k(x),z))*(k(x),*(f(y),z)) → *(f(y),*(k(x),z))*(g(x),*(f(y),z)) → *(f(y),*(g(x),z))*(one,x) → x,*(i(x),x) → one*(*(x,y),z) → *(x,*(y,z))*(g(x),f(y)) → *(f(y),g(x))*(k(x),f(y)) → *(f(y),k(x))*(k(x),h(y)) → *(h(y),k(x))*(k(x),g(y)) → *(g(y),k(x))) |
LS94_G0 | ∞ |
0.40
Statisticsiterations: 4 equalities (active): 53 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.175 time/normalization: 0.083 time/overlaps: 0.099 time/orientation constraints: 0.1 time/project: 0 time/sat: 0.009 time/update context: 0.01 Convergent TRS(VAR x y z)
Completion of LS94_G0
(RULES f(i(x),x) → ef(x,i(x)) → eb(a(b(x))) → a(b(a(x)))i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,i(e) → ef(i(x),f(x,y)) → y,f(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(e,x) → x,a(a(x)) → x,b(b(x)) → x,) |
6.32
Statisticsiterations: 15 equalities (active): 117 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.01 time/maxk: 3.565 time/normalization: 1.347 time/overlaps: 0.739 time/orientation constraints: 2.384 time/project: 0 time/sat: 0.17 time/update context: 0.036 Convergent TRS(VAR x y z)
Completion of LS94_G0
(RULES f(i(x),x) → ef(x,i(x)) → ea(b(a(x))) → b(a(b(x)))i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,i(e) → ef(i(x),f(x,y)) → y,f(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(e,x) → x,a(a(x)) → x,b(b(x)) → x,) |
6.55
Statisticsiterations: 7 equalities (active): 78 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.017 time/maxk: 4.076 time/normalization: 1.101 time/overlaps: 0.765 time/orientation constraints: 2.292 time/project: 0 time/sat: 0.16 time/update context: 0.145 Convergent TRS(VAR x y z)
Completion of LS94_G0
(RULES f(i(x),x) → ef(x,i(x)) → ea(b(a(x))) → b(a(b(x)))i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,i(e) → ef(i(x),f(x,y)) → y,f(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(e,x) → x,a(a(x)) → x,b(b(x)) → x,) |
0.80
Statisticsiterations: 4 equalities (active): 53 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.617 time/normalization: 0.061 time/overlaps: 0.083 time/orientation constraints: 0.149 time/project: 0 time/sat: 0.113 time/update context: 0.004 Convergent TRS(VAR x y z)
Completion of LS94_G0
(RULES f(i(x),x) → ef(x,i(x)) → ea(b(a(x))) → b(a(b(x)))i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,i(e) → ef(i(x),f(x,y)) → y,f(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(e,x) → x,a(a(x)) → x,b(b(x)) → x,) |
0.74
Statisticsiterations: 4 equalities (active): 53 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.549 time/normalization: 0.05 time/overlaps: 0.079 time/orientation constraints: 0.095 time/project: 0 time/sat: 0.083 time/update context: 0.009 Convergent TRS(VAR x y z)
Completion of LS94_G0
(RULES f(i(x),x) → ef(x,i(x)) → ea(b(a(x))) → b(a(b(x)))i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,i(e) → ef(i(x),f(x,y)) → y,f(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(e,x) → x,a(a(x)) → x,b(b(x)) → x,) |
LS94_G1 | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ |
LS94_P1 | ∞ | ∞ |
40.45
Statisticsiterations: 20 equalities (active): 332 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.388 time/maxk: 32.793 time/normalization: 3.043 time/overlaps: 1.646 time/orientation constraints: 10.645 time/project: 0 time/sat: 12.138 time/update context: 0.224 Convergent TRS(VAR x y z)
Completion of LS94_P1
(RULES f(i(x),x) → ef(x,i(x)) → eT(x) → x,S(x) → x,r(x) → x,t(x) → x,s(x) → x,R(x) → x,i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,i(e) → ef(i(x),f(x,y)) → y,f(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(e,x) → x,f(x,e) → x,) |
113.12
Statisticsiterations: 17 equalities (active): 278 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.286 time/maxk: 104.626 time/normalization: 4.543 time/overlaps: 1.251 time/orientation constraints: 6.815 time/project: 0 time/sat: 64.21 time/update context: 5.915 Convergent TRS(VAR x y z)
Completion of LS94_P1
(RULES f(i(x),x) → ef(x,i(x)) → eT(x) → x,S(x) → x,t(x) → x,s(x) → x,r(x) → x,R(x) → x,i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,i(e) → ef(i(x),f(x,y)) → y,f(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(e,x) → x,f(x,e) → x,) |
∞ | ∞ |
Les83_fib |
0.05
Statisticsiterations: 1 equalities (active): 9 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.029 time/normalization: 0.004 time/overlaps: 0.005 time/orientation constraints: 0.018 time/project: 0 time/sat: 0.006 time/update context: 0 Convergent TRS(VAR x y z)
Completion of Les83_fib
(RULES +(s(x),y) → s(+(x,y))+(0,x) → x,+(+(x,y),z) → +(x,+(y,z))fib(0) → 0fib(s(0)) → s(0)fib(s(s(x))) → +(fib(x),fib(s(x)))dfib(0,x) → x,dfib(s(0),x) → s(x)dfib(s(s(x)),y) → dfib(s(x),dfib(x,y))) |
0.13
Statisticsiterations: 2 equalities (active): 23 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.114 time/normalization: 0.002 time/overlaps: 0.004 time/orientation constraints: 0.063 time/project: 0 time/sat: 0.035 time/update context: 0 Convergent TRS(VAR x y z)
Completion of Les83_fib
(RULES +(s(x),y) → s(+(x,y))+(0,x) → x,+(+(x,y),z) → +(x,+(y,z))fib(0) → 0fib(s(0)) → s(0)fib(s(s(x))) → +(fib(x),fib(s(x)))dfib(0,x) → x,dfib(s(0),x) → s(x)dfib(s(s(x)),y) → dfib(s(x),dfib(x,y))) |
0.05
Statisticsiterations: 1 equalities (active): 9 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.029 time/normalization: 0.004 time/overlaps: 0.007 time/orientation constraints: 0.019 time/project: 0 time/sat: 0.004 time/update context: 0 Convergent TRS(VAR x y z)
Completion of Les83_fib
(RULES +(s(x),y) → s(+(x,y))+(0,x) → x,+(+(x,y),z) → +(x,+(y,z))fib(0) → 0fib(s(0)) → s(0)fib(s(s(x))) → +(fib(x),fib(s(x)))dfib(0,x) → x,dfib(s(0),x) → s(x)dfib(s(s(x)),y) → dfib(s(x),dfib(x,y))) |
0.03
Statisticsiterations: 1 equalities (active): 9 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.018 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y z)
Completion of Les83_fib
(RULES +(s(x),y) → s(+(x,y))+(0,x) → x,+(+(x,y),z) → +(x,+(y,z))fib(0) → 0fib(s(0)) → s(0)fib(s(s(x))) → +(fib(x),fib(s(x)))dfib(0,x) → x,dfib(s(0),x) → s(x)dfib(s(s(x)),y) → dfib(s(x),dfib(x,y))) |
0.03
Statisticsiterations: 1 equalities (active): 9 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.021 time/normalization: 0.002 time/overlaps: 0.004 time/orientation constraints: 0.015 time/project: 0 time/sat: 0.003 time/update context: 0 Convergent TRS(VAR x y z)
Completion of Les83_fib
(RULES +(s(x),y) → s(+(x,y))+(0,x) → x,+(+(x,y),z) → +(x,+(y,z))fib(0) → 0fib(s(0)) → s(0)fib(s(s(x))) → +(fib(x),fib(s(x)))dfib(0,x) → x,dfib(s(0),x) → s(x)dfib(s(s(x)),y) → dfib(s(x),dfib(x,y))) |
0.03
Statisticsiterations: 1 equalities (active): 9 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.017 time/normalization: 0.001 time/overlaps: 0.004 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y z)
Completion of Les83_fib
(RULES +(s(x),y) → s(+(x,y))+(0,x) → x,+(+(x,y),z) → +(x,+(y,z))fib(0) → 0fib(s(0)) → s(0)fib(s(s(x))) → +(fib(x),fib(s(x)))dfib(0,x) → x,dfib(s(0),x) → s(x)dfib(s(s(x)),y) → dfib(s(x),dfib(x,y))) |
Les83_subset |
0.04
Statisticsiterations: 1 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.026 time/normalization: 0 time/overlaps: 0.003 time/orientation constraints: 0.015 time/project: 0 time/sat: 0.007 time/update context: 0 Convergent TRS(VAR x y u)
Completion of Les83_subset
(RULES if(tt,x,y) → x,if(ff,x,y) → y,if(x,y,y) → y,if(x,tt,ff) → x,eq(0,0) → tteq(0,s(x)) → ffeq(s(x),0) → ffeq(s(x),s(y)) → eq(x,y)has(empty,x) → ffhas(+(x,y),u) → if(eq(y,u),tt,has(x,u))subset(empty,x) → ttsubset(+(x,y),u) → if(has(u,y),subset(x,u),ff)) |
0.30
Statisticsiterations: 2 equalities (active): 26 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.27 time/normalization: 0.001 time/overlaps: 0.011 time/orientation constraints: 0.082 time/project: 0 time/sat: 0.163 time/update context: 0.002 Convergent TRS(VAR x y u)
Completion of Les83_subset
(RULES if(tt,x,y) → x,if(ff,x,y) → y,if(x,y,y) → y,if(x,tt,ff) → x,eq(0,0) → tteq(0,s(x)) → ffeq(s(x),0) → ffeq(s(x),s(y)) → eq(x,y)has(empty,x) → ffhas(+(x,y),u) → if(eq(y,u),tt,has(x,u))subset(empty,x) → ttsubset(+(x,y),u) → if(has(u,y),subset(x,u),ff)) |
0.05
Statisticsiterations: 1 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.034 time/normalization: 0 time/overlaps: 0.009 time/orientation constraints: 0.018 time/project: 0 time/sat: 0.01 time/update context: 0 Convergent TRS(VAR x y u)
Completion of Les83_subset
(RULES if(tt,x,y) → x,if(ff,x,y) → y,if(x,y,y) → y,if(x,tt,ff) → x,eq(0,0) → tteq(0,s(x)) → ffeq(s(x),0) → ffeq(s(x),s(y)) → eq(x,y)has(empty,x) → ffhas(+(x,y),u) → if(eq(y,u),tt,has(x,u))subset(empty,x) → ttsubset(+(x,y),u) → if(has(u,y),subset(x,u),ff)) |
63.44
Statisticsiterations: 25 equalities (active): 121 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.093 time/maxk: 14.8 time/normalization: 3.363 time/overlaps: 35.145 time/orientation constraints: 5.206 time/project: 0 time/sat: 2.269 time/update context: 0.584 Convergent TRS(VAR x y u)
Completion of Les83_subset
(RULES if(tt,x,y) → x,if(ff,x,y) → y,if(x,y,y) → y,if(x,tt,ff) → x,eq(0,0) → tteq(0,s(x)) → ffeq(s(x),0) → ffeq(s(x),s(y)) → eq(x,y)has(empty,x) → ffhas(+(x,y),u) → if(eq(y,u),tt,has(x,u))subset(empty,x) → ttsubset(+(x,y),u) → if(has(u,y),subset(x,u),ff)) |
0.05
Statisticsiterations: 1 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.037 time/normalization: 0 time/overlaps: 0.005 time/orientation constraints: 0.02 time/project: 0 time/sat: 0.011 time/update context: 0 Convergent TRS(VAR x y u)
Completion of Les83_subset
(RULES if(tt,x,y) → x,if(ff,x,y) → y,if(x,y,y) → y,if(x,tt,ff) → x,eq(0,0) → tteq(0,s(x)) → ffeq(s(x),0) → ffeq(s(x),s(y)) → eq(x,y)has(empty,x) → ffhas(+(x,y),u) → if(eq(y,u),tt,has(x,u))subset(empty,x) → ttsubset(+(x,y),u) → if(has(u,y),subset(x,u),ff)) |
1.22
Statisticsiterations: 3 equalities (active): 61 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 1.155 time/normalization: 0.006 time/overlaps: 0.019 time/orientation constraints: 0.269 time/project: 0 time/sat: 0.791 time/update context: 0.005 Convergent TRS(VAR x y u)
Completion of Les83_subset
(RULES tt → eq(0,0)if(eq(0,0),x,y) → x,if(x,eq(0,0),ff) → x,has(+(x,y),u) → if(eq(y,u),eq(0,0),has(x,u))if(ff,x,y) → y,if(x,y,y) → y,eq(0,s(x)) → ffeq(s(x),0) → ffeq(s(x),s(y)) → eq(x,y)has(empty,x) → ffsubset(empty,x) → eq(0,0)subset(+(x,y),u) → if(has(u,y),subset(x,u),ff)) |
OKW95_dt1_theory | ∞ |
3.69
Statisticsiterations: 6 equalities (active): 105 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 3.568 time/normalization: 0.039 time/overlaps: 0.015 time/orientation constraints: 0.841 time/project: 0 time/sat: 2.001 time/update context: 0.057 Convergent TRS(VAR x y)
Completion of OKW95_dt1_theory
(RULES fib(s(s(x))) → +(fib(s(x)),fib(x))p(x) → -(x,s(0))fib(0) → s(0)fib(s(0)) → s(0)dfib(0) → s(0)dfib(s(0)) → s(0)dfib(s(s(x))) → +(dfib(s(x)),+(dfib(x),dfib(x)))+(x,s(y)) → s(+(x,y))+(x,0) → x,-(s(x),s(y)) → -(x,y)-(x,0) → x,) |
∞ | ∞ | ∞ | ∞ |
SK90_3.01 | ∞ |
3.76
Statisticsiterations: 10 equalities (active): 186 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 3.445 time/normalization: 0.12 time/overlaps: 0.099 time/orientation constraints: 0.709 time/project: 0 time/sat: 0.661 time/update context: 0.14 Convergent TRS(VAR y x z)
Completion of SK90_3.01
(RULES i(*(y,x)) → *(i(x),i(y))i(one) → onei(i(y)) → y,*(y,one) → y,*(y,*(i(y),x)) → x,*(y,i(y)) → one*(i(y),*(y,x)) → x,*(one,y) → y,*(i(y),y) → one*(*(y,x),z) → *(y,*(x,z))div(y,x) → *(y,i(x))) |
556.78
Statisticsiterations: 73 equalities (active): 245 equalities (passive): 0 restarts: 2 time/cache: 0 time/set ops: 2.354 time/maxk: 206.558 time/normalization: 203.289 time/overlaps: 29.031 time/orientation constraints: 60.589 time/project: 0 time/sat: 12.641 time/update context: 2.293 Convergent TRS(VAR y x z)
Completion of SK90_3.01
(RULES i(*(y,x)) → *(i(x),i(y))i(one) → onei(i(y)) → y,*(y,i(y)) → one*(y,one) → y,*(y,*(i(y),x)) → x,*(i(y),*(y,x)) → x,*(one,y) → y,*(i(y),y) → one*(*(y,x),z) → *(y,*(x,z))div(y,x) → *(y,i(x))) |
11.82
Statisticsiterations: 14 equalities (active): 259 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.022 time/maxk: 9.759 time/normalization: 0.769 time/overlaps: 0.655 time/orientation constraints: 1.879 time/project: 0 time/sat: 0.253 time/update context: 0.609 Convergent TRS(VAR y x z)
Completion of SK90_3.01
(RULES i(*(y,x)) → *(i(x),i(y))i(one) → onei(i(y)) → y,*(y,one) → y,*(y,i(y)) → one*(y,*(i(y),x)) → x,*(i(y),*(y,x)) → x,*(one,y) → y,*(i(y),y) → one*(*(y,x),z) → *(y,*(x,z))div(y,x) → *(y,i(x))) |
64.00
Statisticsiterations: 15 equalities (active): 257 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.028 time/maxk: 62.103 time/normalization: 0.775 time/overlaps: 0.438 time/orientation constraints: 2.395 time/project: 0 time/sat: 29.237 time/update context: 0.129 Convergent TRS(VAR y x z)
Completion of SK90_3.01
(RULES *(y,i(y)) → one*(y,*(i(y),x)) → x,i(*(y,x)) → *(i(x),i(y))i(one) → onei(i(y)) → y,*(y,one) → y,*(i(y),*(y,x)) → x,*(one,y) → y,*(i(y),y) → one*(*(y,x),z) → *(y,*(x,z))div(y,x) → *(y,i(x))) |
226.59
Statisticsiterations: 18 equalities (active): 297 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.074 time/maxk: 217.71 time/normalization: 6.001 time/overlaps: 1.292 time/orientation constraints: 3.482 time/project: 0 time/sat: 123.705 time/update context: 2.526 Convergent TRS(VAR y x z)
Completion of SK90_3.01
(RULES i(*(y,x)) → *(i(x),i(y))i(one) → onei(i(y)) → y,*(y,one) → y,*(y,i(y)) → one*(y,*(i(y),x)) → x,*(i(y),*(y,x)) → x,*(one,y) → y,*(i(y),y) → one*(*(y,x),z) → *(y,*(x,z))div(y,x) → *(y,i(x))) |
SK90_3.02 |
0.02
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.006 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.02
(RULES +(x,+(y,z)) → +(+(x,y),z)f(+(x,y)) → +(f(x),f(y))f(f(x)) → x,) |
0.02
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.015 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.02
(RULES +(x,+(y,z)) → +(+(x,y),z)f(+(x,y)) → +(f(x),f(y))f(f(x)) → x,) |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.006 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.02
(RULES f(+(x,y)) → +(f(x),f(y))f(f(x)) → x,+(+(x,y),z) → +(x,+(y,z))) |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.02
(RULES f(+(x,y)) → +(f(x),f(y))f(f(x)) → x,+(+(x,y),z) → +(x,+(y,z))) |
0.02
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.006 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.02
(RULES f(+(x,y)) → +(f(x),f(y))f(f(x)) → x,+(+(x,y),z) → +(x,+(y,z))) |
0.02
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.01 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.008 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.02
(RULES f(+(x,y)) → +(f(x),f(y))f(f(x)) → x,+(+(x,y),z) → +(x,+(y,z))) |
SK90_3.03 | ∞ |
59.04
Statisticsiterations: 13 equalities (active): 216 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.077 time/maxk: 48.129 time/normalization: 7.755 time/overlaps: 2.046 time/orientation constraints: 4.39 time/project: 0 time/sat: 20.26 time/update context: 2.923 Convergent TRS(VAR y x z)
Completion of SK90_3.03
(RULES i(i(y)) → y,d(y,x) → *(y,i(x))i(*(y,x)) → *(i(x),i(y))*(y,i(y)) → one*(y,*(i(y),x)) → x,*(i(y),*(y,x)) → x,*(*(y,x),z) → *(y,*(x,z))*(y,one) → y,i(one) → one*(one,y) → y,*(i(y),y) → one) |
17.42
Statisticsiterations: 14 equalities (active): 254 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.055 time/maxk: 11.845 time/normalization: 2.956 time/overlaps: 1.333 time/orientation constraints: 4.36 time/project: 0 time/sat: 1.314 time/update context: 0.134 Convergent TRS(VAR y x z)
Completion of SK90_3.03
(RULES i(i(y)) → y,d(y,x) → *(y,i(x))i(*(y,x)) → *(i(x),i(y))*(y,*(i(y),x)) → x,*(*(y,x),z) → *(y,*(x,z))*(i(y),*(y,x)) → x,*(y,one) → y,*(y,i(y)) → onei(one) → one*(one,y) → y,*(i(y),y) → one) |
159.38
Statisticsiterations: 28 equalities (active): 126 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.316 time/maxk: 81.933 time/normalization: 62.718 time/overlaps: 6.088 time/orientation constraints: 10.538 time/project: 0 time/sat: 1.18 time/update context: 6.709 Convergent TRS(VAR y x z)
Completion of SK90_3.03
(RULES d(y,x) → *(y,i(x))i(*(y,x)) → *(i(x),i(y))*(y,*(i(y),x)) → x,*(i(y),*(y,x)) → x,*(*(y,x),z) → *(y,*(x,z))*(y,one) → y,*(y,i(y)) → onei(one) → onei(i(y)) → y,*(one,y) → y,*(i(y),y) → one) |
28.76
Statisticsiterations: 10 equalities (active): 163 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.017 time/maxk: 26.413 time/normalization: 1.165 time/overlaps: 0.629 time/orientation constraints: 2.569 time/project: 0 time/sat: 14.027 time/update context: 0.063 Convergent TRS(VAR y x z)
Completion of SK90_3.03
(RULES i(i(y)) → y,d(y,x) → *(y,i(x))i(*(y,x)) → *(i(x),i(y))*(y,*(i(y),x)) → x,*(*(y,x),z) → *(y,*(x,z))*(i(y),*(y,x)) → x,*(y,one) → y,*(y,i(y)) → onei(one) → one*(one,y) → y,*(i(y),y) → one) |
2.10
Statisticsiterations: 5 equalities (active): 97 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 1.879 time/normalization: 0.075 time/overlaps: 0.093 time/orientation constraints: 0.301 time/project: 0 time/sat: 0.454 time/update context: 0.037 Convergent TRS(VAR y x z)
Completion of SK90_3.03
(RULES i(i(y)) → y,d(y,x) → *(y,i(x))i(*(y,x)) → *(i(x),i(y))*(y,*(i(y),x)) → x,*(i(y),*(y,x)) → x,*(*(y,x),z) → *(y,*(x,z))*(y,one) → y,*(y,i(y)) → onei(one) → one*(one,y) → y,*(i(y),y) → one) |
SK90_3.04 | ∞ |
5.24
Statisticsiterations: 9 equalities (active): 153 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.06 time/maxk: 2.577 time/normalization: 1.094 time/overlaps: 0.645 time/orientation constraints: 0.646 time/project: 0 time/sat: 0.327 time/update context: 0.208 Convergent TRS(VAR x y z)
Completion of SK90_3.04
(RULES *(f(*(x,y)),z) → *(f(y),*(f(x),z))*(x,*(f(x),y)) → y,*(f(one),x) → x,*(f(f(x)),y) → *(x,y)*(f(x),*(x,y)) → y,*(*(x,y),z) → *(x,*(y,z))*(one,x) → x,g(x) → *(f(x),x)) |
10.92
Statisticsiterations: 11 equalities (active): 165 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.174 time/maxk: 3.719 time/normalization: 2.979 time/overlaps: 1.416 time/orientation constraints: 1.376 time/project: 0 time/sat: 0.204 time/update context: 0.061 Convergent TRS(VAR x y z)
Completion of SK90_3.04
(RULES *(f(*(x,y)),z) → *(f(y),*(f(x),z))*(x,*(f(x),y)) → y,*(f(one),x) → x,*(f(f(x)),y) → *(x,y)*(f(x),*(x,y)) → y,*(*(x,y),z) → *(x,*(y,z))*(one,x) → x,g(x) → *(f(x),x)) |
6.25
Statisticsiterations: 11 equalities (active): 156 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.055 time/maxk: 3.476 time/normalization: 1.245 time/overlaps: 0.625 time/orientation constraints: 0.937 time/project: 0 time/sat: 0.12 time/update context: 0.29 Convergent TRS(VAR x y z)
Completion of SK90_3.04
(RULES *(f(*(x,y)),z) → *(f(y),*(f(x),z))*(x,*(f(x),y)) → y,*(f(one),x) → x,*(f(f(x)),y) → *(x,y)*(f(x),*(x,y)) → y,*(*(x,y),z) → *(x,*(y,z))*(one,x) → x,g(x) → *(f(x),x)) |
128.88
Statisticsiterations: 11 equalities (active): 163 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.089 time/maxk: 126.026 time/normalization: 1.126 time/overlaps: 0.693 time/orientation constraints: 0.955 time/project: 0 time/sat: 102.917 time/update context: 0.048 Convergent TRS(VAR x y z)
Completion of SK90_3.04
(RULES *(f(*(x,y)),z) → *(f(y),*(f(x),z))g(x) → *(f(x),x)*(x,*(f(x),y)) → y,*(f(one),x) → x,*(f(f(x)),y) → *(x,y)*(f(x),*(x,y)) → y,*(*(x,y),z) → *(x,*(y,z))*(one,x) → x,) |
112.57
Statisticsiterations: 11 equalities (active): 171 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.111 time/maxk: 107.689 time/normalization: 2.135 time/overlaps: 0.984 time/orientation constraints: 0.86 time/project: 0 time/sat: 72.079 time/update context: 0.441 Convergent TRS(VAR x y z)
Completion of SK90_3.04
(RULES *(f(*(x,y)),z) → *(f(y),*(f(x),z))*(x,*(f(x),y)) → y,*(f(one),x) → x,*(f(f(x)),y) → *(x,y)*(f(x),*(x,y)) → y,*(*(x,y),z) → *(x,*(y,z))*(one,x) → x,g(x) → *(f(x),x)) |
SK90_3.05 |
11.29
Statisticsiterations: 8 equalities (active): 95 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.017 time/maxk: 0.484 time/normalization: 2.073 time/overlaps: 1.156 time/orientation constraints: 0.331 time/project: 0 time/sat: 0.041 time/update context: 0.015 Convergent TRS(VAR y x z)
Completion of SK90_3.05
(RULES f(g(y)) → g(y)*(f(y),y) → f(y)*(y,g(y)) → g(y)f(*(y,x)) → g(y)*(*(y,x),z) → *(f(x),z)g(*(y,x)) → f(x)*(y,f(x)) → *(y,x)*(y,*(x,z)) → *(y,g(x))g(g(y)) → g(y)g(f(y)) → f(y)f(f(y)) → f(y)*(f(y),g(y)) → y,*(g(y),x) → *(y,x)) |
∞ |
3.24
Statisticsiterations: 10 equalities (active): 112 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.016 time/maxk: 1.973 time/normalization: 0.491 time/overlaps: 0.261 time/orientation constraints: 0.842 time/project: 0 time/sat: 0.073 time/update context: 0.043 Convergent TRS(VAR y x z)
Completion of SK90_3.05
(RULES *(y,g(y)) → g(y)f(g(y)) → g(y)*(f(y),y) → f(y)f(*(y,x)) → g(y)*(*(y,x),z) → *(f(x),z)g(*(y,x)) → f(x)*(y,f(x)) → *(y,x)*(y,*(x,z)) → *(y,g(x))f(f(y)) → f(y)g(f(y)) → f(y)g(g(y)) → g(y)*(f(y),g(y)) → y,*(g(y),x) → *(y,x)) |
2.40
Statisticsiterations: 8 equalities (active): 117 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 1.708 time/normalization: 0.245 time/overlaps: 0.204 time/orientation constraints: 0.511 time/project: 0 time/sat: 0.059 time/update context: 0.094 Convergent TRS(VAR y x z)
Completion of SK90_3.05
(RULES f(g(y)) → g(y)*(y,g(y)) → g(y)f(*(y,x)) → g(y)*(f(y),y) → f(y)*(*(y,x),z) → *(f(x),z)g(*(y,x)) → f(x)*(y,f(x)) → *(y,x)*(y,*(x,z)) → *(y,g(x))g(f(y)) → f(y)f(f(y)) → f(y)g(g(y)) → g(y)*(f(y),g(y)) → y,*(g(y),x) → *(y,x)) |
∞ | ∞ |
SK90_3.06 | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ |
SK90_3.07 | ∞ |
5.02
Statisticsiterations: 10 equalities (active): 119 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.01 time/maxk: 4.594 time/normalization: 0.173 time/overlaps: 0.125 time/orientation constraints: 1.428 time/project: 0 time/sat: 0.821 time/update context: 0.205 Convergent TRS(VAR x y z)
Completion of SK90_3.07
(RULES +(x,-(x)) → 0+(-(x),x) → 0+(-(x),+(x,y)) → y,-(+(x,y)) → +(-(y),-(x))g(x,y) → f(x,+(x,-(y)),y)+(x,+(-(x),y)) → y,-(0) → 0-(-(x)) → x,+(x,0) → x,+(0,x) → x,+(+(x,y),z) → +(x,+(y,z))f(0,x,y) → x,) |
42.96
Statisticsiterations: 44 equalities (active): 136 equalities (passive): 0 restarts: 2 time/cache: 0 time/set ops: 0.246 time/maxk: 29.998 time/normalization: 6.582 time/overlaps: 2.46 time/orientation constraints: 13.828 time/project: 0 time/sat: 3.353 time/update context: 0.349 Convergent TRS(VAR x y z)
Completion of SK90_3.07
(RULES +(x,-(x)) → 0+(-(x),x) → 0+(x,+(-(x),y)) → y,+(-(x),+(x,y)) → y,-(+(x,y)) → +(-(y),-(x))g(x,y) → f(x,+(x,-(y)),y)-(0) → 0+(x,0) → x,+(0,x) → x,-(-(x)) → x,+(+(x,y),z) → +(x,+(y,z))f(0,x,y) → x,) |
142.87
Statisticsiterations: 63 equalities (active): 191 equalities (passive): 0 restarts: 3 time/cache: 0 time/set ops: 0.433 time/maxk: 108.608 time/normalization: 17.52 time/overlaps: 5.095 time/orientation constraints: 21.09 time/project: 0 time/sat: 4.069 time/update context: 12.085 Convergent TRS(VAR x y z)
Completion of SK90_3.07
(RULES +(x,-(x)) → 0+(-(x),x) → 0g(x,y) → f(x,+(x,-(y)),y)-(+(x,y)) → +(-(y),-(x))+(-(x),+(x,y)) → y,-(0) → 0-(-(x)) → x,+(x,+(-(x),y)) → y,+(x,0) → x,+(0,x) → x,+(+(x,y),z) → +(x,+(y,z))f(0,x,y) → x,) |
6.85
Statisticsiterations: 9 equalities (active): 130 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 6.471 time/normalization: 0.126 time/overlaps: 0.141 time/orientation constraints: 1.224 time/project: 0 time/sat: 1.002 time/update context: 0.03 Convergent TRS(VAR x y z)
Completion of SK90_3.07
(RULES +(x,-(x)) → 0+(-(x),x) → 0-(+(x,y)) → +(-(y),-(x))g(x,y) → f(x,+(x,-(y)),y)+(-(x),+(x,y)) → y,+(x,+(-(x),y)) → y,-(0) → 0+(x,0) → x,+(0,x) → x,-(-(x)) → x,+(+(x,y),z) → +(x,+(y,z))f(0,x,y) → x,) |
28.89
Statisticsiterations: 14 equalities (active): 177 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.021 time/maxk: 27.472 time/normalization: 0.53 time/overlaps: 0.343 time/orientation constraints: 2.374 time/project: 0 time/sat: 7.03 time/update context: 0.459 Convergent TRS(VAR x y z)
Completion of SK90_3.07
(RULES +(x,-(x)) → 0+(-(x),x) → 0+(x,+(-(x),y)) → y,-(+(x,y)) → +(-(y),-(x))g(x,y) → f(x,+(x,-(y)),y)+(-(x),+(x,y)) → y,-(0) → 0+(x,0) → x,+(0,x) → x,-(-(x)) → x,+(+(x,y),z) → +(x,+(y,z))f(0,x,y) → x,) |
SK90_3.08 |
0.04
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.019 time/normalization: 0.001 time/overlaps: 0.006 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR y x)
Completion of SK90_3.08
(RULES \(y,x) → *(x,y)*(*(y,x),y) → x,/(y,x) → *(x,y)*(y,*(x,y)) → x,) |
0.02
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.011 time/normalization: 0.001 time/overlaps: 0.004 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.001 time/update context: 0.001 Convergent TRS(VAR y x)
Completion of SK90_3.08
(RULES \(y,x) → *(x,y)*(*(y,x),y) → x,/(y,x) → *(x,y)*(y,*(x,y)) → x,) |
0.02
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.01 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.003 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR y x)
Completion of SK90_3.08
(RULES \(y,x) → *(x,y)*(*(y,x),y) → x,/(y,x) → *(x,y)*(y,*(x,y)) → x,) |
0.02
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.01 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.005 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR y x)
Completion of SK90_3.08
(RULES \(y,x) → *(x,y)*(*(y,x),y) → x,/(y,x) → *(x,y)*(y,*(x,y)) → x,) |
0.02
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.014 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR y x)
Completion of SK90_3.08
(RULES \(y,x) → *(x,y)*(*(y,x),y) → x,/(y,x) → *(x,y)*(y,*(x,y)) → x,) |
0.02
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.012 time/normalization: 0 time/overlaps: 0.004 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR y x)
Completion of SK90_3.08
(RULES \(y,x) → *(x,y)*(*(y,x),y) → x,/(y,x) → *(x,y)*(y,*(x,y)) → x,) |
SK90_3.10 |
0.01
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.002 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR y x)
Completion of SK90_3.10
(RULES f(y,y) → oneg(y,y) → one*(y,one) → y,*(one,y) → y,g(y,one) → y,f(y,*(y,x)) → x,f(one,y) → y,g(*(y,x),x) → y,) |
0.01
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR y x)
Completion of SK90_3.10
(RULES g(y,y) → onef(y,y) → onef(one,y) → y,g(y,one) → y,f(y,*(y,x)) → x,g(*(y,x),x) → y,*(y,one) → y,*(one,y) → y,) |
0.01
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR y x)
Completion of SK90_3.10
(RULES g(y,y) → onef(y,y) → onef(one,y) → y,g(y,one) → y,f(y,*(y,x)) → x,g(*(y,x),x) → y,*(y,one) → y,*(one,y) → y,) |
0.01
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR y x)
Completion of SK90_3.10
(RULES g(y,y) → onef(y,y) → onef(one,y) → y,g(y,one) → y,f(y,*(y,x)) → x,g(*(y,x),x) → y,*(y,one) → y,*(one,y) → y,) |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR y x)
Completion of SK90_3.10
(RULES g(y,y) → onef(y,y) → onef(one,y) → y,g(y,one) → y,f(y,*(y,x)) → x,g(*(y,x),x) → y,*(y,one) → y,*(one,y) → y,) |
0.01
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR y x)
Completion of SK90_3.10
(RULES g(y,y) → onef(y,y) → onef(one,y) → y,g(y,one) → y,f(y,*(y,x)) → x,g(*(y,x),x) → y,*(y,one) → y,*(one,y) → y,) |
SK90_3.11 |
0.05
Statisticsiterations: 3 equalities (active): 15 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.029 time/normalization: 0.001 time/overlaps: 0.006 time/orientation constraints: 0.02 time/project: 0 time/sat: 0.004 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.11
(RULES p(x) → x,s(x) → x,+(x,0) → x,) |
0.06
Statisticsiterations: 3 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.053 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.034 time/project: 0 time/sat: 0.003 time/update context: 0.003 Convergent TRS(VAR x)
Completion of SK90_3.11
(RULES p(x) → x,s(x) → x,+(x,0) → x,) |
0.02
Statisticsiterations: 3 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.014 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.11
(RULES p(x) → x,s(x) → x,+(x,0) → x,) |
0.05
Statisticsiterations: 3 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.04 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.025 time/project: 0 time/sat: 0.002 time/update context: 0.001 Convergent TRS(VAR x)
Completion of SK90_3.11
(RULES p(x) → x,s(x) → x,+(x,0) → x,) |
0.03
Statisticsiterations: 3 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.024 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.016 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.11
(RULES p(x) → x,s(x) → x,+(x,0) → x,) |
0.12
Statisticsiterations: 3 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.1 time/normalization: 0.001 time/overlaps: 0.004 time/orientation constraints: 0.063 time/project: 0 time/sat: 0.006 time/update context: 0.002 Convergent TRS(VAR x)
Completion of SK90_3.11
(RULES p(x) → x,s(x) → x,+(x,0) → x,) |
SK90_3.12 | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ |
SK90_3.13 |
0.12
Statisticsiterations: 2 equalities (active): 17 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.053 time/normalization: 0.014 time/overlaps: 0.022 time/orientation constraints: 0.033 time/project: 0 time/sat: 0.012 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.13
(RULES 1 → exp(0)+(x,+(y,z)) → +(+(x,y),z)*(x,exp(0)) → x,*(x,*(exp(0),y)) → *(x,y)+(x,0) → x,*(*(x,y),z) → *(x,*(y,z))exp(+(x,y)) → *(exp(x),exp(y))) |
0.02
Statisticsiterations: 1 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.007 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.13
(RULES *(x,*(y,z)) → *(*(x,y),z)+(x,+(y,z)) → +(+(x,y),z)+(x,0) → x,*(x,1) → x,exp(0) → 1exp(+(x,y)) → *(exp(x),exp(y))) |
0.07
Statisticsiterations: 2 equalities (active): 13 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.028 time/normalization: 0.005 time/overlaps: 0.005 time/orientation constraints: 0.019 time/project: 0 time/sat: 0.004 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.13
(RULES +(x,+(y,z)) → +(+(x,y),z)*(x,*(1,y)) → *(x,y)+(x,0) → x,*(*(x,y),z) → *(x,*(y,z))*(x,1) → x,exp(0) → 1exp(+(x,y)) → *(exp(x),exp(y))) |
0.04
Statisticsiterations: 1 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.024 time/normalization: 0.005 time/overlaps: 0.002 time/orientation constraints: 0.018 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.13
(RULES *(x,*(y,z)) → *(*(x,y),z)+(x,+(y,z)) → +(+(x,y),z)+(x,0) → x,*(x,1) → x,exp(0) → 1exp(+(x,y)) → *(exp(x),exp(y))) |
0.10
Statisticsiterations: 2 equalities (active): 13 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.05 time/normalization: 0.007 time/overlaps: 0.009 time/orientation constraints: 0.031 time/project: 0 time/sat: 0.008 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.13
(RULES *(exp(x),exp(y)) → exp(+(x,y))+(x,+(0,y)) → +(x,y)*(exp(x),*(exp(y),z)) → *(exp(+(x,y)),z)*(x,*(1,y)) → *(x,y)exp(+(0,x)) → *(1,exp(x))+(+(x,y),z) → +(x,+(y,z))+(x,0) → x,*(*(x,y),z) → *(x,*(y,z))*(x,1) → x,exp(0) → 1) |
0.03
Statisticsiterations: 1 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.017 time/normalization: 0.004 time/overlaps: 0.003 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.13
(RULES *(x,*(y,z)) → *(*(x,y),z)+(x,+(y,z)) → +(+(x,y),z)+(x,0) → x,*(x,1) → x,exp(0) → 1exp(+(x,y)) → *(exp(x),exp(y))) |
SK90_3.14 |
0.08
Statisticsiterations: 2 equalities (active): 15 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.053 time/normalization: 0.005 time/overlaps: 0.009 time/orientation constraints: 0.031 time/project: 0 time/sat: 0.014 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.14
(RULES s(0) → h(0)f(g(x,y),0) → g(s(x),y)s(h(0)) → 0f(h(0),x) → s(x)f(f(x,0),0) → x,g(h(0),x) → f(x,0)s(s(x)) → x,f(0,x) → x,f(s(x),y) → s(f(x,y))g(0,x) → x,) |
0.14
Statisticsiterations: 2 equalities (active): 17 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.101 time/normalization: 0.003 time/overlaps: 0.008 time/orientation constraints: 0.032 time/project: 0 time/sat: 0.056 time/update context: 0.001 Convergent TRS(VAR x y)
Completion of SK90_3.14
(RULES f(f(x,0),0) → x,s(s(x)) → x,f(0,x) → x,f(s(x),y) → s(f(x,y))g(0,x) → x,g(s(x),y) → f(g(x,y),0)h(0) → s(0)) |
0.07
Statisticsiterations: 2 equalities (active): 16 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.058 time/normalization: 0 time/overlaps: 0.003 time/orientation constraints: 0.038 time/project: 0 time/sat: 0.01 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.14
(RULES s(0) → h(0)s(h(0)) → 0f(h(0),x) → s(x)f(f(x,0),0) → x,g(h(0),x) → f(x,0)s(s(x)) → x,f(0,x) → x,f(s(x),y) → s(f(x,y))g(0,x) → x,g(s(x),y) → f(g(x,y),0)) |
0.07
Statisticsiterations: 2 equalities (active): 17 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.06 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.035 time/project: 0 time/sat: 0.013 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.14
(RULES s(0) → h(0)s(h(0)) → 0f(h(0),x) → s(x)f(f(x,0),0) → x,g(h(0),x) → f(x,0)s(s(x)) → x,f(0,x) → x,f(s(x),y) → s(f(x,y))g(0,x) → x,g(s(x),y) → f(g(x,y),0)) |
0.29
Statisticsiterations: 4 equalities (active): 51 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.264 time/normalization: 0.005 time/overlaps: 0.007 time/orientation constraints: 0.138 time/project: 0 time/sat: 0.056 time/update context: 0.002 Convergent TRS(VAR x y)
Completion of SK90_3.14
(RULES f(x,0) → g(h(0),x)s(x) → f(h(0),x)f(f(h(0),x),y) → f(h(0),f(x,y))g(h(0),h(0)) → h(0)g(h(0),f(h(0),x)) → f(h(0),g(h(0),x))g(h(0),0) → 0f(h(0),h(0)) → 0f(h(0),f(h(0),x)) → x,g(h(0),g(x,y)) → g(f(h(0),x),y)f(0,x) → x,g(0,x) → x,) |
∞ |
SK90_3.15 |
0.03
Statisticsiterations: 2 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.022 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.012 time/project: 0 time/sat: 0.003 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.15
(RULES eq(p(x),x) → falseeq(x,s(y)) → eq(p(x),y)eq(x,p(x)) → falseeq(s(x),y) → eq(x,p(y))eq(x,x) → truep(s(x)) → x,eq(p(x),p(y)) → eq(x,y)) |
0.06
Statisticsiterations: 2 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.046 time/normalization: 0.002 time/overlaps: 0.004 time/orientation constraints: 0.034 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.15
(RULES eq(p(x),x) → falseeq(x,p(x)) → falseeq(x,s(y)) → eq(p(x),y)eq(s(x),y) → eq(x,p(y))p(s(x)) → x,eq(x,x) → trueeq(p(x),p(y)) → eq(x,y)) |
0.02
Statisticsiterations: 2 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.014 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.009 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.15
(RULES eq(p(x),x) → falseeq(x,p(x)) → falseeq(x,s(y)) → eq(p(x),y)eq(s(x),y) → eq(x,p(y))p(s(x)) → x,eq(x,x) → trueeq(p(x),p(y)) → eq(x,y)) |
0.03
Statisticsiterations: 2 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.017 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.15
(RULES eq(p(x),x) → falseeq(x,p(x)) → falseeq(x,s(y)) → eq(p(x),y)eq(s(x),y) → eq(x,p(y))p(s(x)) → x,eq(x,x) → trueeq(p(x),p(y)) → eq(x,y)) |
0.03
Statisticsiterations: 2 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.023 time/normalization: 0 time/overlaps: 0.003 time/orientation constraints: 0.014 time/project: 0 time/sat: 0.004 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.15
(RULES eq(p(x),x) → falseeq(x,p(x)) → falseeq(x,s(y)) → eq(p(x),y)eq(s(x),y) → eq(x,p(y))p(s(x)) → x,eq(x,x) → trueeq(p(x),p(y)) → eq(x,y)) |
0.05
Statisticsiterations: 2 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.034 time/normalization: 0.001 time/overlaps: 0.004 time/orientation constraints: 0.015 time/project: 0 time/sat: 0.005 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.15
(RULES eq(p(x),x) → falseeq(x,p(x)) → falseeq(x,s(y)) → eq(p(x),y)eq(s(x),y) → eq(x,p(y))p(s(x)) → x,eq(x,x) → trueeq(p(x),p(y)) → eq(x,y)) |
SK90_3.16 |
0.01
Statisticsiterations: 2 equalities (active): 7 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.16
(RULES .(car(x),cdr(x)) → x,atom(x) → falsecar(.(x,y)) → x,cdr(.(x,y)) → y,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.16
(RULES atom(x) → falsecar(.(x,y)) → x,cdr(.(x,y)) → y,.(car(x),cdr(x)) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.16
(RULES atom(x) → falsecar(.(x,y)) → x,cdr(.(x,y)) → y,.(car(x),cdr(x)) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.16
(RULES atom(x) → falsecar(.(x,y)) → x,cdr(.(x,y)) → y,.(car(x),cdr(x)) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.16
(RULES atom(x) → falsecar(.(x,y)) → x,cdr(.(x,y)) → y,.(car(x),cdr(x)) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.16
(RULES atom(x) → falsecar(.(x,y)) → x,cdr(.(x,y)) → y,.(car(x),cdr(x)) → x,) |
SK90_3.17 |
0.03
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.019 time/normalization: 0.001 time/overlaps: 0.002 time/orientation constraints: 0.013 time/project: 0 time/sat: 0.003 time/update context: 0 Convergent TRS(VAR x z y)
Completion of SK90_3.17
(RULES or(&(x,z),&(y,z)) → &(or(x,y),z)or(&(x,z),z) → &(or(x,z),z)or(x,&(z,x)) → &(or(x,z),x)&(x,x) → x,or(x,x) → x,) |
0.05
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.037 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.032 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x z y)
Completion of SK90_3.17
(RULES or(&(x,z),&(y,z)) → &(or(x,y),z)or(&(x,z),z) → &(or(x,z),z)or(x,&(z,x)) → &(or(x,z),x)&(x,x) → x,or(x,x) → x,) |
0.03
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.019 time/normalization: 0.001 time/overlaps: 0.002 time/orientation constraints: 0.015 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x z y)
Completion of SK90_3.17
(RULES or(&(x,z),&(y,z)) → &(or(x,y),z)or(&(x,z),z) → &(or(x,z),z)or(x,&(z,x)) → &(or(x,z),x)&(x,x) → x,or(x,x) → x,) |
0.03
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.018 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.014 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x z y)
Completion of SK90_3.17
(RULES or(&(x,z),&(y,z)) → &(or(x,y),z)or(&(x,z),z) → &(or(x,z),z)or(x,&(z,x)) → &(or(x,z),x)&(x,x) → x,or(x,x) → x,) |
0.03
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.021 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.016 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x z y)
Completion of SK90_3.17
(RULES or(&(x,z),&(y,z)) → &(or(x,y),z)or(&(x,z),z) → &(or(x,z),z)or(x,&(z,x)) → &(or(x,z),x)&(x,x) → x,or(x,x) → x,) |
0.03
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.02 time/normalization: 0.001 time/overlaps: 0.002 time/orientation constraints: 0.014 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x z y)
Completion of SK90_3.17
(RULES or(&(x,z),&(y,z)) → &(or(x,y),z)or(&(x,z),z) → &(or(x,z),z)or(x,&(z,x)) → &(or(x,z),x)&(x,x) → x,or(x,x) → x,) |
SK90_3.18 | ∞ |
0.21
Statisticsiterations: 3 equalities (active): 24 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.182 time/normalization: 0.003 time/overlaps: 0.007 time/orientation constraints: 0.123 time/project: 0 time/sat: 0.041 time/update context: 0.001 Convergent TRS(VAR y x z)
Completion of SK90_3.18
(RULES @(.(y,x),z) → .(y,@(x,z))rev(@(y,.(x,nil))) → .(x,rev(y))@(nil,y) → y,rev(nil) → nilrev(.(y,x)) → @(rev(x),.(y,nil))rev(rev(y)) → y,) |
∞ | ∞ |
0.26
Statisticsiterations: 3 equalities (active): 24 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.236 time/normalization: 0.004 time/overlaps: 0.006 time/orientation constraints: 0.165 time/project: 0 time/sat: 0.043 time/update context: 0 Convergent TRS(VAR y x z)
Completion of SK90_3.18
(RULES @(.(y,x),z) → .(y,@(x,z))rev(@(y,.(x,nil))) → .(x,rev(y))@(nil,y) → y,rev(nil) → nilrev(.(y,x)) → @(rev(x),.(y,nil))rev(rev(y)) → y,) |
0.35
Statisticsiterations: 3 equalities (active): 24 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.324 time/normalization: 0.004 time/overlaps: 0.008 time/orientation constraints: 0.2 time/project: 0 time/sat: 0.081 time/update context: 0.002 Convergent TRS(VAR y x z)
Completion of SK90_3.18
(RULES @(.(y,x),z) → .(y,@(x,z))rev(@(y,.(x,nil))) → .(x,rev(y))@(nil,y) → y,rev(nil) → nilrev(.(y,x)) → @(rev(x),.(y,nil))rev(rev(y)) → y,) |
SK90_3.19 |
0.25
Statisticsiterations: 2 equalities (active): 31 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.11 time/normalization: 0.021 time/overlaps: 0.085 time/orientation constraints: 0.063 time/project: 0 time/sat: 0.033 time/update context: 0 Convergent TRS(VAR y x z)
Completion of SK90_3.19
(RULES @(.(y,x),z) → .(y,@(x,z))@(reviter(y,x),z) → reviter(y,@(x,z))@(nil,y) → y,@(@(y,x),z) → @(y,@(x,z))reviter(nil,y) → y,reviter(.(y,x),z) → reviter(x,.(y,z))rev(y) → reviter(y,nil)) |
0.20
Statisticsiterations: 2 equalities (active): 34 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.178 time/normalization: 0.003 time/overlaps: 0.007 time/orientation constraints: 0.081 time/project: 0 time/sat: 0.066 time/update context: 0.002 Convergent TRS(VAR y x z)
Completion of SK90_3.19
(RULES @(.(y,x),z) → .(y,@(x,z))@(reviter(y,x),z) → reviter(y,@(x,z))@(nil,y) → y,@(@(y,x),z) → @(y,@(x,z))reviter(nil,y) → y,reviter(.(y,x),z) → reviter(x,.(y,z))rev(y) → reviter(y,nil)) |
10.17
Statisticsiterations: 19 equalities (active): 94 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.042 time/maxk: 7.244 time/normalization: 0.998 time/overlaps: 1.14 time/orientation constraints: 4.774 time/project: 0 time/sat: 0.582 time/update context: 0.04 Convergent TRS(VAR y x z)
Completion of SK90_3.19
(RULES @(.(y,x),z) → .(y,@(x,z))@(reviter(y,x),z) → reviter(y,@(x,z))@(nil,y) → y,@(@(y,x),z) → @(y,@(x,z))reviter(nil,y) → y,reviter(.(y,x),z) → reviter(x,.(y,z))rev(y) → reviter(y,nil)) |
0.17
Statisticsiterations: 2 equalities (active): 31 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.121 time/normalization: 0.013 time/overlaps: 0.02 time/orientation constraints: 0.08 time/project: 0 time/sat: 0.018 time/update context: 0.002 Convergent TRS(VAR y x z)
Completion of SK90_3.19
(RULES @(.(y,x),z) → .(y,@(x,z))@(reviter(y,x),z) → reviter(y,@(x,z))@(nil,y) → y,@(@(y,x),z) → @(y,@(x,z))reviter(nil,y) → y,reviter(.(y,x),z) → reviter(x,.(y,z))rev(y) → reviter(y,nil)) |
0.99
Statisticsiterations: 4 equalities (active): 61 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.814 time/normalization: 0.051 time/overlaps: 0.048 time/orientation constraints: 0.512 time/project: 0 time/sat: 0.076 time/update context: 0.003 Convergent TRS(VAR y x z)
Completion of SK90_3.19
(RULES @(.(y,x),z) → .(y,@(x,z))@(reviter(y,x),z) → reviter(y,@(x,z))@(nil,y) → y,@(@(y,x),z) → @(y,@(x,z))reviter(nil,y) → y,reviter(.(y,x),z) → reviter(x,.(y,z))rev(y) → reviter(y,nil)) |
0.19
Statisticsiterations: 2 equalities (active): 31 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.152 time/normalization: 0.006 time/overlaps: 0.012 time/orientation constraints: 0.092 time/project: 0 time/sat: 0.024 time/update context: 0.002 Convergent TRS(VAR y x z)
Completion of SK90_3.19
(RULES @(.(y,x),z) → .(y,@(x,z))@(reviter(y,x),z) → reviter(y,@(x,z))@(nil,y) → y,@(@(y,x),z) → @(y,@(x,z))reviter(nil,y) → y,reviter(.(y,x),z) → reviter(x,.(y,z))rev(y) → reviter(y,nil)) |
SK90_3.20 | ∞ |
0.22
Statisticsiterations: 2 equalities (active): 37 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.194 time/normalization: 0.001 time/overlaps: 0.004 time/orientation constraints: 0.083 time/project: 0 time/sat: 0.088 time/update context: 0.003 Convergent TRS(VAR x y z v)
Completion of SK90_3.20
(RULES eq(end(x,y),end(z,v)) → and(eq(y,v),eq(x,z))eq(end(x,y),nil) → falseeq(nil,end(x,y)) → falseand(true,true) → trueeq(x,x) → truef(x,nil) → end(nil,x)f(x,end(y,z)) → end(f(x,y),z).(nil,x) → x,.(end(x,y),z) → .(x,f(y,z))null(nil) → truenull(end(x,y)) → false) |
∞ |
101.29
Statisticsiterations: 52 equalities (active): 112 equalities (passive): 0 restarts: 3 time/cache: 0 time/set ops: 0.789 time/maxk: 30.068 time/normalization: 3.686 time/overlaps: 53.736 time/orientation constraints: 14.782 time/project: 0 time/sat: 3.841 time/update context: 0.828 Convergent TRS(VAR x y z v)
Completion of SK90_3.20
(RULES eq(end(x,y),end(z,v)) → and(eq(y,v),eq(x,z))eq(end(x,y),nil) → falseeq(nil,end(x,y)) → falseand(true,true) → trueeq(x,x) → truef(x,nil) → end(nil,x)f(x,end(y,z)) → end(f(x,y),z).(nil,x) → x,.(end(x,y),z) → .(x,f(y,z))null(nil) → truenull(end(x,y)) → false) |
3.89
Statisticsiterations: 6 equalities (active): 101 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.008 time/maxk: 3.378 time/normalization: 0.063 time/overlaps: 0.29 time/orientation constraints: 1.603 time/project: 0 time/sat: 0.738 time/update context: 0.016 Convergent TRS(VAR x y z v)
Completion of SK90_3.20
(RULES true → null(nil)eq(end(x,y),end(z,v)) → and(eq(y,v),eq(x,z))eq(end(x,y),nil) → falseeq(nil,end(x,y)) → falseeq(x,x) → null(nil)and(null(nil),null(nil)) → null(nil)f(x,nil) → end(nil,x)f(x,end(y,z)) → end(f(x,y),z).(nil,x) → x,.(end(x,y),z) → .(x,f(y,z))null(end(x,y)) → false) |
1.07
Statisticsiterations: 4 equalities (active): 79 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 0.894 time/normalization: 0.018 time/overlaps: 0.085 time/orientation constraints: 0.488 time/project: 0 time/sat: 0.149 time/update context: 0.013 Convergent TRS(VAR x y z v)
Completion of SK90_3.20
(RULES eq(end(x,y),end(z,v)) → and(eq(y,v),eq(x,z))eq(end(x,y),nil) → falseeq(nil,end(x,y)) → falseand(true,true) → trueeq(x,x) → truef(x,nil) → end(nil,x)f(x,end(y,z)) → end(f(x,y),z).(nil,x) → x,.(end(x,y),z) → .(x,f(y,z))null(nil) → truenull(end(x,y)) → false) |
SK90_3.21 |
2.10
Statisticsiterations: 3 equalities (active): 77 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.072 time/maxk: 0.269 time/normalization: 0.477 time/overlaps: 0.57 time/orientation constraints: 0.194 time/project: 0 time/sat: 0.03 time/update context: 0.003 Convergent TRS(VAR x y)
Completion of SK90_3.21
(RULES g(x,y) → x,f(x,nil) → nilcons(x,nil) → x,cdr(nil) → nil) |
0.77
Statisticsiterations: 3 equalities (active): 73 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.647 time/normalization: 0.045 time/overlaps: 0.027 time/orientation constraints: 0.326 time/project: 0 time/sat: 0.202 time/update context: 0.012 Convergent TRS(VAR x y)
Completion of SK90_3.21
(RULES g(x,y) → x,f(x,nil) → nilcons(x,nil) → x,cdr(nil) → nil) |
0.93
Statisticsiterations: 3 equalities (active): 80 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 0.684 time/normalization: 0.091 time/overlaps: 0.055 time/orientation constraints: 0.5 time/project: 0 time/sat: 0.044 time/update context: 0.005 Convergent TRS(VAR x y)
Completion of SK90_3.21
(RULES f(x,nil) → nilg(x,y) → x,cons(x,nil) → x,cdr(nil) → nil) |
0.63
Statisticsiterations: 3 equalities (active): 69 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.46 time/normalization: 0.064 time/overlaps: 0.038 time/orientation constraints: 0.283 time/project: 0 time/sat: 0.029 time/update context: 0.016 Convergent TRS(VAR x y)
Completion of SK90_3.21
(RULES g(x,y) → x,f(x,nil) → nilcons(x,nil) → x,cdr(nil) → nil) |
1.16
Statisticsiterations: 3 equalities (active): 80 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 0.875 time/normalization: 0.091 time/overlaps: 0.064 time/orientation constraints: 0.493 time/project: 0 time/sat: 0.076 time/update context: 0.005 Convergent TRS(VAR x y)
Completion of SK90_3.21
(RULES f(x,nil) → nilg(x,y) → x,cons(x,nil) → x,cdr(nil) → nil) |
1.24
Statisticsiterations: 3 equalities (active): 83 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 1.05 time/normalization: 0.068 time/overlaps: 0.06 time/orientation constraints: 0.465 time/project: 0 time/sat: 0.05 time/update context: 0.034 Convergent TRS(VAR x y)
Completion of SK90_3.21
(RULES f(x,nil) → nilg(x,y) → x,cons(x,nil) → x,cdr(nil) → nil) |
SK90_3.22 |
10.30
Statisticsiterations: 5 equalities (active): 99 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.252 time/maxk: 1.921 time/normalization: 3.872 time/overlaps: 1.016 time/orientation constraints: 0.959 time/project: 0 time/sat: 0.822 time/update context: 0.013 Convergent TRS(VAR x)
Completion of SK90_3.22
(RULES d(c(x)) → b(x)a(x) → c(b(x))e(x) → c(b(b(x)))d(d(x)) → c(c(b(x)))b(b(b(x))) → c(x)b(c(x)) → c(b(x))c(d(x)) → b(x)b(d(x)) → d(b(x))c(c(c(x))) → d(x)) |
∞ |
270.97
Statisticsiterations: 34 equalities (active): 531 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.308 time/maxk: 269.038 time/normalization: 0.798 time/overlaps: 0.334 time/orientation constraints: 25.194 time/project: 0 time/sat: 163.989 time/update context: 0.902 Convergent TRS(VAR x)
Completion of SK90_3.22
(RULES e(d(x)) → c(x)a(a(d(x))) → c(c(x))e(b(x)) → c(c(x))b(e(x)) → c(c(x))e(e(e(x))) → a(x)d(e(x)) → c(x)d(a(x)) → a(d(x))e(c(x)) → a(a(x))d(d(d(x))) → e(x)d(c(x)) → b(x)d(b(x)) → e(e(x))a(a(a(x))) → b(x)a(b(x)) → e(x)b(c(x)) → a(x)c(c(c(x))) → d(x)c(a(x)) → d(d(x))c(d(x)) → b(x)e(a(x)) → d(x)c(e(x)) → a(a(x))b(d(x)) → e(e(x))b(b(x)) → a(d(x))a(c(x)) → d(d(x))a(e(x)) → d(x)b(a(x)) → e(x)c(b(x)) → a(x)) |
471.81
Statisticsiterations: 28 equalities (active): 447 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.199 time/maxk: 467.673 time/normalization: 3.27 time/overlaps: 0.143 time/orientation constraints: 14.68 time/project: 0 time/sat: 205.304 time/update context: 7.084 Convergent TRS(VAR x)
Completion of SK90_3.22
(RULES e(d(x)) → c(x)e(e(e(x))) → a(x)d(c(x)) → b(x)d(b(x)) → e(e(x))d(e(x)) → c(x)b(b(b(x))) → c(x)a(d(x)) → b(b(x))e(c(x)) → a(a(x))d(a(x)) → b(b(x))d(d(d(x))) → e(x)a(a(a(x))) → b(x)b(a(x)) → e(x)b(e(x)) → e(b(x))e(b(b(x))) → d(d(x))e(a(x)) → d(x)a(b(x)) → e(x)b(c(x)) → a(x)c(a(x)) → d(d(x))c(d(x)) → b(x)c(c(x)) → e(b(x))a(c(x)) → d(d(x))c(e(x)) → a(a(x))b(d(x)) → e(e(x))a(e(x)) → d(x)c(b(x)) → a(x)) |
173.34
Statisticsiterations: 21 equalities (active): 426 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.143 time/maxk: 172.126 time/normalization: 0.424 time/overlaps: 0.201 time/orientation constraints: 11.083 time/project: 0 time/sat: 74.301 time/update context: 0.332 Convergent TRS(VAR x)
Completion of SK90_3.22
(RULES e(d(x)) → c(x)e(b(x)) → c(c(x))e(e(e(x))) → a(x)d(b(x)) → e(e(x))d(d(d(x))) → e(x)d(e(x)) → c(x)d(c(x)) → b(x)b(e(x)) → c(c(x))a(c(x)) → d(d(x))a(a(a(x))) → b(x)e(c(x)) → a(a(x))d(a(a(x))) → c(c(x))c(c(c(x))) → d(x)b(d(x)) → e(e(x))b(a(x)) → e(x)c(d(x)) → b(x)b(c(x)) → a(x)a(d(x)) → d(a(x))c(a(x)) → d(d(x))e(a(x)) → d(x)a(b(x)) → e(x)c(e(x)) → a(a(x))b(b(x)) → d(a(x))a(e(x)) → d(x)c(b(x)) → a(x)) |
190.02
Statisticsiterations: 17 equalities (active): 347 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.085 time/maxk: 187.957 time/normalization: 1.389 time/overlaps: 0.141 time/orientation constraints: 9.1 time/project: 0 time/sat: 33.66 time/update context: 3.606 Convergent TRS(VAR x)
Completion of SK90_3.22
(RULES e(d(x)) → c(x)d(c(x)) → b(x)b(e(x)) → c(c(x))e(c(x)) → c(e(x))d(b(x)) → e(e(x))e(b(x)) → c(c(x))d(d(x)) → c(e(e(e(x))))d(e(x)) → c(x)c(b(x)) → e(e(e(x)))b(b(x)) → c(e(e(x)))c(d(x)) → b(x)e(e(e(e(x)))) → d(x)b(c(x)) → e(e(e(x)))c(c(e(e(x)))) → e(x)c(c(c(x))) → d(x)a(x) → e(e(e(x)))b(d(x)) → e(e(x))) |
SK90_3.23 |
114.20
Statisticsiterations: 15 equalities (active): 275 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 4.663 time/maxk: 9.835 time/normalization: 24.785 time/overlaps: 31.097 time/orientation constraints: 5.619 time/project: 0 time/sat: 3.295 time/update context: 0.105 Convergent TRS(VAR x)
Completion of SK90_3.23
(RULES d(a(a(x))) → a(d(a(x)))d(a(c(x))) → a(x)b(a(x)) → a(c(x))c(a(x)) → a(c(x))c(d(a(x))) → a(x)b(d(x)) → x,e(x) → d(a(x))) |
2.52
Statisticsiterations: 9 equalities (active): 49 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 2.493 time/normalization: 0.005 time/overlaps: 0.005 time/orientation constraints: 0.336 time/project: 0 time/sat: 1.993 time/update context: 0.008 Convergent TRS(VAR x)
Completion of SK90_3.23
(RULES d(a(a(x))) → a(d(a(x)))d(a(c(x))) → a(x)b(a(x)) → a(c(x))c(a(x)) → a(c(x))c(d(a(x))) → a(x)b(d(x)) → x,e(x) → d(a(x))) |
0.27
Statisticsiterations: 6 equalities (active): 39 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.245 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.172 time/project: 0 time/sat: 0.029 time/update context: 0.002 Convergent TRS(VAR x)
Completion of SK90_3.23
(RULES d(a(c(x))) → a(x)b(a(x)) → a(c(x))d(a(a(x))) → a(d(a(x)))c(d(a(x))) → a(x)c(a(x)) → a(c(x))b(d(x)) → x,e(x) → d(a(x))) |
0.06
Statisticsiterations: 3 equalities (active): 18 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.048 time/normalization: 0.001 time/overlaps: 0.002 time/orientation constraints: 0.029 time/project: 0 time/sat: 0.007 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.23
(RULES d(a(x)) → e(x)e(a(x)) → a(e(x))b(e(x)) → a(x)b(a(x)) → a(c(x))c(a(x)) → a(c(x))e(c(x)) → a(x)b(d(x)) → x,c(e(x)) → a(x)) |
0.49
Statisticsiterations: 6 equalities (active): 48 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.456 time/normalization: 0.003 time/overlaps: 0.005 time/orientation constraints: 0.286 time/project: 0 time/sat: 0.06 time/update context: 0.003 Convergent TRS(VAR x)
Completion of SK90_3.23
(RULES d(a(c(x))) → a(x)d(a(a(x))) → a(d(a(x)))b(a(x)) → a(c(x))c(d(a(x))) → a(x)c(a(x)) → a(c(x))b(d(x)) → x,e(x) → d(a(x))) |
0.79
Statisticsiterations: 8 equalities (active): 74 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.734 time/normalization: 0.006 time/overlaps: 0.015 time/orientation constraints: 0.418 time/project: 0 time/sat: 0.073 time/update context: 0.01 Convergent TRS(VAR x)
Completion of SK90_3.23
(RULES e(c(x)) → a(x)d(a(x)) → e(x)b(e(x)) → a(x)e(a(x)) → a(e(x))b(a(x)) → a(c(x))c(a(x)) → a(c(x))b(d(x)) → x,c(e(x)) → a(x)) |
SK90_3.24 |
0.02
Statisticsiterations: 2 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.014 time/normalization: 0.003 time/overlaps: 0.003 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.24
(RULES a(x) → c(x)b(x) → c(x)c(c(c(x))) → c(c(x))) |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.015 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.007 time/project: 0 time/sat: 0.003 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.24
(RULES a(x) → b(x)b(b(b(x))) → b(b(x))c(x) → b(x)) |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.014 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.24
(RULES b(x) → c(x)a(x) → c(x)c(c(c(x))) → c(c(x))) |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.001 time/update context: 0.001 Convergent TRS(VAR x)
Completion of SK90_3.24
(RULES a(x) → b(x)b(b(b(x))) → b(b(x))c(x) → b(x)) |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.015 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.24
(RULES b(x) → c(x)a(x) → c(x)c(c(c(x))) → c(c(x))) |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.24
(RULES a(x) → b(x)b(b(b(x))) → b(b(x))c(x) → b(x)) |
SK90_3.25 |
0.02
Statisticsiterations: 2 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.012 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.25
(RULES a(a(a(b(x)))) → a(b(a(a(x))))a(b(a(a(b(x))))) → a(x)) |
0.02
Statisticsiterations: 2 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.25
(RULES a(a(a(b(x)))) → a(b(a(a(x))))a(b(a(a(b(x))))) → a(x)) |
0.01
Statisticsiterations: 2 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.25
(RULES a(a(a(b(x)))) → a(b(a(a(x))))a(b(a(a(b(x))))) → a(x)) |
0.02
Statisticsiterations: 2 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.014 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.012 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.25
(RULES a(a(a(b(x)))) → a(b(a(a(x))))a(b(a(a(b(x))))) → a(x)) |
0.01
Statisticsiterations: 2 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.01 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.25
(RULES a(a(a(b(x)))) → a(b(a(a(x))))a(b(a(a(b(x))))) → a(x)) |
0.02
Statisticsiterations: 2 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.011 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.008 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.25
(RULES a(a(a(b(x)))) → a(b(a(a(x))))a(b(a(a(b(x))))) → a(x)) |
SK90_3.26 | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ |
SK90_3.27 |
13.41
Statisticsiterations: 3 equalities (active): 85 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 2.615 time/maxk: 0.828 time/normalization: 4.347 time/overlaps: 0.901 time/orientation constraints: 0.625 time/project: 0 time/sat: 0.122 time/update context: 0.005 Convergent TRS(VAR x)
Completion of SK90_3.27
(RULES b(x) → x,a(x) → x,c(x) → x,) |
7.74
Statisticsiterations: 5 equalities (active): 102 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.022 time/maxk: 7.389 time/normalization: 0.22 time/overlaps: 0.023 time/orientation constraints: 1.68 time/project: 0 time/sat: 3.559 time/update context: 0.294 Convergent TRS(VAR x)
Completion of SK90_3.27
(RULES a(x) → x,c(x) → x,b(x) → x,) |
4.77
Statisticsiterations: 5 equalities (active): 127 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.038 time/maxk: 4.305 time/normalization: 0.169 time/overlaps: 0.076 time/orientation constraints: 2.638 time/project: 0 time/sat: 0.555 time/update context: 0.023 Convergent TRS(VAR x)
Completion of SK90_3.27
(RULES b(x) → x,c(x) → x,a(x) → x,) |
1.96
Statisticsiterations: 3 equalities (active): 90 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.02 time/maxk: 1.626 time/normalization: 0.172 time/overlaps: 0.04 time/orientation constraints: 0.852 time/project: 0 time/sat: 0.104 time/update context: 0.115 Convergent TRS(VAR x)
Completion of SK90_3.27
(RULES c(x) → x,a(x) → x,b(x) → x,) |
15.69
Statisticsiterations: 7 equalities (active): 141 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.043 time/maxk: 15.285 time/normalization: 0.166 time/overlaps: 0.061 time/orientation constraints: 3.234 time/project: 0 time/sat: 5.374 time/update context: 0.035 Convergent TRS(VAR x)
Completion of SK90_3.27
(RULES c(x) → x,b(x) → x,a(x) → x,) |
11.89
Statisticsiterations: 7 equalities (active): 131 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.036 time/maxk: 11.376 time/normalization: 0.308 time/overlaps: 0.038 time/orientation constraints: 2.158 time/project: 0 time/sat: 2.167 time/update context: 0.329 Convergent TRS(VAR x)
Completion of SK90_3.27
(RULES c(x) → x,b(x) → x,a(x) → x,) |
SK90_3.28 | ∞ |
382.27
Statisticsiterations: 16 equalities (active): 269 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.039 time/maxk: 381.466 time/normalization: 0.468 time/overlaps: 0.039 time/orientation constraints: 4.949 time/project: 0 time/sat: 337.191 time/update context: 1.344 Convergent TRS(VAR x)
Completion of SK90_3.28
(RULES a(w(x)) → c(a(x))u(x) → c(v(w(a(v(x)))))b(x) → c(v(w(x)))a(v(a(x))) → v(x)a(c(x)) → w(a(x))a(v(v(x))) → v(v(a(x)))a(v(w(x))) → c(c(v(v(w(a(v(x)))))))v(w(w(x))) → w(w(v(x)))v(w(v(x))) → w(x)v(c(x)) → c(c(v(w(x))))c(w(x)) → x,w(c(x)) → x,) |
∞ | ∞ | ∞ |
596.62
Statisticsiterations: 16 equalities (active): 336 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.071 time/maxk: 594.602 time/normalization: 0.912 time/overlaps: 0.501 time/orientation constraints: 9.588 time/project: 0 time/sat: 477.772 time/update context: 2.034 Convergent TRS(VAR x)
Completion of SK90_3.28
(RULES a(w(x)) → c(a(x))u(x) → c(v(w(a(v(x)))))a(c(x)) → w(a(x))b(x) → c(v(w(x)))a(v(a(x))) → v(x)a(v(v(x))) → v(v(a(x)))a(v(w(x))) → c(c(v(v(w(a(v(x)))))))v(w(w(x))) → w(w(v(x)))v(w(v(x))) → w(x)v(c(x)) → c(c(v(w(x))))c(w(x)) → x,w(c(x)) → x,) |
SK90_3.29 |
1.16
Statisticsiterations: 4 equalities (active): 66 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.703 time/normalization: 0.032 time/overlaps: 0.268 time/orientation constraints: 0.516 time/project: 0 time/sat: 0.128 time/update context: 0.005 Convergent TRS(VAR x)
Completion of SK90_3.29
(RULES c(w(x)) → d(w(x))a(d(x)) → v(a(x))a(c(x)) → e(a(x))e(a(w(x))) → e(b(w(x)))v(a(w(x))) → e(b(w(x)))v(b(w(x))) → e(b(w(x)))b(c(x)) → e(b(x))b(d(x)) → v(b(x))u(x) → d(w(x))) |
1.43
Statisticsiterations: 5 equalities (active): 54 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 1.404 time/normalization: 0.004 time/overlaps: 0.005 time/orientation constraints: 0.278 time/project: 0 time/sat: 0.999 time/update context: 0.009 Convergent TRS(VAR x)
Completion of SK90_3.29
(RULES d(w(x)) → c(w(x))e(b(w(x))) → a(c(w(x)))v(b(w(x))) → a(c(w(x)))e(a(x)) → a(c(x))v(a(x)) → a(d(x))b(c(x)) → e(b(x))b(d(x)) → v(b(x))u(x) → c(w(x))) |
140.56
Statisticsiterations: 55 equalities (active): 149 equalities (passive): 0 restarts: 2 time/cache: 0 time/set ops: 0.1 time/maxk: 63.749 time/normalization: 0.758 time/overlaps: 74.419 time/orientation constraints: 24.332 time/project: 0 time/sat: 19.921 time/update context: 0.266 Convergent TRS(VAR x)
Completion of SK90_3.29
(RULES d(w(x)) → u(x)c(w(x)) → u(x)a(d(x)) → v(a(x))a(c(x)) → e(a(x))e(a(w(x))) → a(u(x))v(a(w(x))) → a(u(x))e(b(w(x))) → a(u(x))v(b(w(x))) → a(u(x))b(c(x)) → e(b(x))b(d(x)) → v(b(x))b(u(x)) → a(u(x))) |
0.55
Statisticsiterations: 5 equalities (active): 54 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.51 time/normalization: 0.003 time/overlaps: 0.007 time/orientation constraints: 0.292 time/project: 0 time/sat: 0.088 time/update context: 0.006 Convergent TRS(VAR x)
Completion of SK90_3.29
(RULES a(d(x)) → v(a(x))a(c(x)) → e(a(x))c(w(x)) → d(w(x))e(b(w(x))) → e(a(w(x)))v(b(w(x))) → e(a(w(x)))v(a(w(x))) → e(a(w(x)))b(c(x)) → e(b(x))b(d(x)) → v(b(x))u(x) → d(w(x))) |
0.88
Statisticsiterations: 5 equalities (active): 56 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.817 time/normalization: 0.004 time/overlaps: 0.015 time/orientation constraints: 0.488 time/project: 0 time/sat: 0.183 time/update context: 0.003 Convergent TRS(VAR x)
Completion of SK90_3.29
(RULES a(d(x)) → v(a(x))a(c(x)) → e(a(x))e(a(w(x))) → e(b(w(x)))v(b(w(x))) → e(b(w(x)))v(a(w(x))) → e(b(w(x)))d(w(x)) → c(w(x))b(c(x)) → e(b(x))b(d(x)) → v(b(x))u(x) → c(w(x))) |
314.83
Statisticsiterations: 68 equalities (active): 282 equalities (passive): 0 restarts: 3 time/cache: 0 time/set ops: 0.139 time/maxk: 270.502 time/normalization: 1.443 time/overlaps: 39.349 time/orientation constraints: 43.768 time/project: 0 time/sat: 159.991 time/update context: 1.941 Convergent TRS(VAR x)
Completion of SK90_3.29
(RULES d(w(x)) → u(x)c(w(x)) → u(x)a(d(x)) → v(a(x))a(c(x)) → e(a(x))e(a(w(x))) → v(a(w(x)))a(u(x)) → v(a(w(x)))v(b(w(x))) → v(a(w(x)))e(b(w(x))) → v(a(w(x)))b(c(x)) → e(b(x))b(d(x)) → v(b(x))b(u(x)) → v(a(w(x)))) |
SK90_3.30 |
0.20
Statisticsiterations: 3 equalities (active): 35 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.118 time/normalization: 0.014 time/overlaps: 0.041 time/orientation constraints: 0.069 time/project: 0 time/sat: 0.036 time/update context: 0.001 Convergent TRS(VAR x y)
Completion of SK90_3.30
(RULES f(g(x),y) → ak(a,a) → ah(x) → a) |
0.05
Statisticsiterations: 3 equalities (active): 13 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.046 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.034 time/project: 0 time/sat: 0.005 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.30
(RULES f(g(x),y) → ak(a,a) → ah(x) → a) |
0.08
Statisticsiterations: 3 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.073 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.059 time/project: 0 time/sat: 0.007 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.30
(RULES k(a,a) → af(g(x),y) → ah(x) → a) |
0.05
Statisticsiterations: 3 equalities (active): 13 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.04 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.03 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.30
(RULES f(g(x),y) → ak(a,a) → ah(x) → a) |
0.08
Statisticsiterations: 3 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.066 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.054 time/project: 0 time/sat: 0.005 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.30
(RULES k(a,a) → af(g(x),y) → ah(x) → a) |
0.05
Statisticsiterations: 3 equalities (active): 13 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.045 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.03 time/project: 0 time/sat: 0.004 time/update context: 0.001 Convergent TRS(VAR x y)
Completion of SK90_3.30
(RULES f(g(x),y) → ak(a,a) → ah(x) → a) |
SK90_3.31 |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.31
(RULES i(x) → g(f(x,x))f(x,h(y)) → j(x)f(h(x),y) → j(h(x))) |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.31
(RULES i(x) → g(f(x,x))f(x,h(y)) → j(x)f(h(x),y) → j(h(x))) |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.004 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.31
(RULES i(x) → g(f(x,x))f(x,h(y)) → j(x)f(h(x),y) → j(h(x))) |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.004 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.31
(RULES i(x) → g(f(x,x))f(x,h(y)) → j(x)f(h(x),y) → j(h(x))) |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.31
(RULES i(x) → g(f(x,x))f(x,h(y)) → j(x)f(h(x),y) → j(h(x))) |
0.02
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.007 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.31
(RULES i(x) → g(f(x,x))f(x,h(y)) → j(x)f(h(x),y) → j(h(x))) |
SK90_3.32 |
0.01
Statisticsiterations: 2 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.006 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.32
(RULES g(g(x)) → x,f(x,y) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.32
(RULES f(x,y) → x,g(g(x)) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.32
(RULES f(x,y) → x,g(g(x)) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.32
(RULES f(x,y) → x,g(g(x)) → x,) |
0.00
Statisticsiterations: 2 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.001 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.32
(RULES f(x,y) → x,g(g(x)) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of SK90_3.32
(RULES f(x,y) → x,g(g(x)) → x,) |
SK90_3.33 |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.33
(RULES g(a) → ag(g(x)) → x,f(x) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.33
(RULES g(a) → af(x) → x,g(g(x)) → x,) |
0.00
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.33
(RULES g(a) → af(x) → x,g(g(x)) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.33
(RULES g(a) → af(x) → x,g(g(x)) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.33
(RULES g(a) → af(x) → x,g(g(x)) → x,) |
0.03
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.019 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.33
(RULES g(a) → af(x) → x,g(g(x)) → x,) |
TPDB_secret2006_torpa_secr10 |
7.55
Statisticsiterations: 4 equalities (active): 85 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.106 time/maxk: 0.692 time/normalization: 2.582 time/overlaps: 0.715 time/orientation constraints: 0.48 time/project: 0 time/sat: 0.124 time/update context: 0.006 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr10
(RULES a(c(a(x))) → c(c(c(x)))a(a(a(x))) → c(c(c(x)))a(a(c(x))) → c(a(c(x)))a(a(b(x))) → c(b(x))c(b(c(c(x)))) → c(c(c(x)))a(b(c(b(x)))) → c(c(b(x)))a(b(c(c(x)))) → c(c(x))b(a(a(x))) → b(c(c(x)))a(c(c(x))) → c(c(c(x)))c(a(a(x))) → c(c(x))b(c(a(c(x)))) → b(c(c(c(x))))c(a(c(b(x)))) → a(c(b(x)))a(b(a(c(b(x))))) → a(c(b(x)))c(c(a(x))) → c(c(c(x)))c(c(c(c(x)))) → c(c(c(x)))c(c(c(b(x)))) → a(c(b(x)))c(b(c(b(x)))) → a(c(b(x)))b(c(c(b(x)))) → b(c(b(x)))c(b(a(x))) → a(a(x))b(a(b(x))) → b(x)) |
30.40
Statisticsiterations: 10 equalities (active): 135 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.013 time/maxk: 30.102 time/normalization: 0.156 time/overlaps: 0.037 time/orientation constraints: 2.125 time/project: 0 time/sat: 24.866 time/update context: 0.177 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr10
(RULES a(a(a(a(x)))) → a(a(a(x)))a(c(a(x))) → a(a(a(x)))c(a(a(x))) → a(b(a(a(x))))b(a(a(c(x)))) → b(a(a(a(x))))a(a(a(c(x)))) → a(a(a(x)))c(a(b(a(a(x))))) → a(a(a(x)))a(b(a(a(a(x))))) → a(a(a(x)))a(a(b(a(x)))) → a(a(x))c(b(x)) → a(a(b(x)))b(a(b(x))) → b(x)c(c(x)) → a(b(a(a(x))))c(a(c(x))) → a(a(c(x)))) |
1.93
Statisticsiterations: 5 equalities (active): 96 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 1.719 time/normalization: 0.086 time/overlaps: 0.043 time/orientation constraints: 1.089 time/project: 0 time/sat: 0.159 time/update context: 0.011 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr10
(RULES a(a(b(x))) → c(b(x))a(b(a(c(b(x))))) → a(c(b(x)))a(a(c(b(x)))) → a(c(b(x)))a(a(a(c(x)))) → a(a(a(x)))b(a(a(c(x)))) → b(a(a(a(x))))c(a(b(c(b(x))))) → a(c(b(x)))a(a(a(a(x)))) → a(a(a(x)))c(a(b(a(a(x))))) → a(a(a(x)))c(c(x)) → a(b(a(a(x))))c(b(c(b(x)))) → a(c(b(x)))c(a(a(x))) → a(b(a(a(x))))a(b(a(a(a(x))))) → a(a(a(x)))c(b(a(x))) → a(a(x))a(c(a(x))) → a(a(a(x)))b(a(b(x))) → b(x)c(a(c(x))) → a(a(c(x)))) |
2.91
Statisticsiterations: 7 equalities (active): 111 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 2.632 time/normalization: 0.142 time/overlaps: 0.056 time/orientation constraints: 0.852 time/project: 0 time/sat: 0.143 time/update context: 0.098 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr10
(RULES a(a(c(x))) → c(a(c(x)))a(a(b(x))) → c(b(x))a(b(c(b(x)))) → c(c(b(x)))b(c(a(c(x)))) → b(c(c(c(x))))a(b(c(c(x)))) → c(c(x))b(a(a(x))) → b(c(c(x)))c(a(a(x))) → c(c(x))a(c(b(x))) → c(c(c(b(x))))a(a(a(x))) → c(c(c(x)))a(c(c(x))) → c(c(c(x)))c(c(a(x))) → c(c(c(x)))c(b(c(b(x)))) → c(c(c(b(x))))a(c(a(x))) → c(c(c(x)))c(b(c(c(x)))) → c(c(c(x)))c(c(c(c(x)))) → c(c(c(x)))b(c(c(b(x)))) → b(c(b(x)))c(b(a(x))) → a(a(x))b(a(b(x))) → b(x)) |
11.25
Statisticsiterations: 9 equalities (active): 154 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.01 time/maxk: 10.866 time/normalization: 0.163 time/overlaps: 0.105 time/orientation constraints: 1.81 time/project: 0 time/sat: 1.753 time/update context: 0.032 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr10
(RULES a(b(a(a(x)))) → c(c(x))a(a(b(x))) → c(b(x))a(c(c(x))) → a(a(a(x)))a(b(a(c(b(x))))) → a(c(b(x)))a(a(c(b(x)))) → a(c(b(x)))b(a(a(c(x)))) → b(a(a(a(x))))a(a(a(c(x)))) → a(a(a(x)))a(a(a(a(x)))) → a(a(a(x)))c(a(b(c(b(x))))) → a(c(b(x)))c(c(c(x))) → a(a(a(x)))b(c(c(x))) → b(a(a(x)))c(a(a(x))) → c(c(x))c(b(c(b(x)))) → a(c(b(x)))c(c(b(x))) → a(b(c(b(x))))c(b(a(x))) → a(a(x))a(c(a(x))) → a(a(a(x)))b(a(b(x))) → b(x)c(c(a(x))) → a(a(a(x)))c(a(c(x))) → a(a(c(x)))) |
9.27
Statisticsiterations: 8 equalities (active): 120 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 8.869 time/normalization: 0.193 time/overlaps: 0.083 time/orientation constraints: 1.257 time/project: 0 time/sat: 0.954 time/update context: 0.157 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr10
(RULES a(a(b(x))) → c(b(x))a(a(a(c(x)))) → a(a(a(x)))a(b(a(a(x)))) → c(c(x))a(a(c(b(x)))) → a(c(b(x)))a(b(a(c(b(x))))) → a(c(b(x)))c(a(b(c(b(x))))) → a(c(b(x)))a(c(c(x))) → a(a(a(x)))a(a(a(a(x)))) → a(a(a(x)))b(a(a(c(x)))) → b(a(a(a(x))))c(c(c(x))) → a(a(a(x)))b(c(c(x))) → b(a(a(x)))c(a(a(x))) → c(c(x))c(b(c(b(x)))) → a(c(b(x)))c(c(a(x))) → a(a(a(x)))c(c(b(x))) → a(b(c(b(x))))c(b(a(x))) → a(a(x))a(c(a(x))) → a(a(a(x)))b(a(b(x))) → b(x)c(a(c(x))) → a(a(c(x)))) |
TPDB_secret2006_torpa_secr4 |
25.12
Statisticsiterations: 6 equalities (active): 140 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.401 time/maxk: 2.412 time/normalization: 7.224 time/overlaps: 2.216 time/orientation constraints: 1.111 time/project: 0 time/sat: 1.038 time/update context: 0.026 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr4
(RULES d(c(c(x))) → a(x)a(d(x)) → a(x)b(b(x)) → a(x)b(d(x)) → c(c(x))d(b(x)) → c(c(x))d(a(x)) → a(x)b(c(c(x))) → a(x)b(a(x)) → a(x)a(b(x)) → a(x)e(a(x)) → a(e(x))c(c(c(x))) → a(x)e(d(x)) → a(e(x))e(c(x)) → a(e(x))e(b(x)) → a(e(x))a(c(x)) → a(x)c(a(x)) → a(x)a(a(x)) → a(x)c(b(x)) → a(x)c(d(x)) → a(x)d(d(x)) → b(x)) |
33.54
Statisticsiterations: 8 equalities (active): 157 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 33.382 time/normalization: 0.052 time/overlaps: 0.01 time/orientation constraints: 1.193 time/project: 0 time/sat: 29.863 time/update context: 0.097 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr4
(RULES b(x) → d(d(x))a(x) → d(d(d(d(x))))c(d(x)) → d(d(d(d(x))))e(c(x)) → d(d(d(d(e(x)))))e(d(x)) → d(d(d(d(e(x)))))d(d(d(c(x)))) → d(d(d(d(x))))c(c(x)) → d(d(d(x)))d(d(d(d(d(x))))) → d(d(d(d(x))))) |
6.70
Statisticsiterations: 7 equalities (active): 148 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.01 time/maxk: 6.439 time/normalization: 0.089 time/overlaps: 0.076 time/orientation constraints: 1.649 time/project: 0 time/sat: 3.407 time/update context: 0.029 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr4
(RULES a(x) → c(d(x))d(b(x)) → c(c(x))c(b(x)) → c(d(x))b(d(x)) → c(c(x))d(c(d(x))) → c(d(x))b(c(d(x))) → c(d(x))c(d(e(x))) → e(c(x))e(b(x)) → e(c(x))e(d(x)) → e(c(x))d(e(c(x))) → e(c(x))c(e(c(x))) → e(c(x))b(e(c(x))) → e(c(x))b(b(x)) → c(d(x))c(c(d(x))) → c(d(x))e(e(c(x))) → e(c(e(x)))e(c(c(x))) → e(c(x))e(c(d(x))) → e(c(x))c(d(c(x))) → c(d(x))c(c(c(x))) → c(d(x))d(c(c(x))) → c(d(x))b(c(c(x))) → c(d(x))d(d(x)) → b(x)) |
2.64
Statisticsiterations: 6 equalities (active): 125 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 2.486 time/normalization: 0.075 time/overlaps: 0.021 time/orientation constraints: 0.931 time/project: 0 time/sat: 0.319 time/update context: 0.058 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr4
(RULES b(x) → d(d(x))a(x) → c(d(x))d(d(d(c(x)))) → c(d(x))c(d(e(x))) → e(d(x))d(c(d(x))) → c(d(x))c(e(d(x))) → e(d(x))d(e(d(x))) → e(d(x))d(d(d(d(x)))) → c(d(x))e(d(c(x))) → e(d(x))e(e(d(x))) → e(d(e(x)))e(c(x)) → e(d(x))c(d(c(x))) → c(d(x))e(d(d(x))) → e(d(x))c(d(d(x))) → c(d(x))c(c(x)) → d(d(d(x)))) |
24.01
Statisticsiterations: 12 equalities (active): 206 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.016 time/maxk: 23.631 time/normalization: 0.132 time/overlaps: 0.129 time/orientation constraints: 2.939 time/project: 0 time/sat: 11.526 time/update context: 0.071 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr4
(RULES b(x) → d(d(x))d(d(d(x))) → c(c(x))d(c(c(x))) → c(c(c(x)))c(d(x)) → c(c(c(x)))e(d(x)) → e(c(x))c(c(c(e(x)))) → e(c(x))c(e(c(x))) → e(c(x))a(x) → c(c(c(x)))d(e(c(x))) → e(c(x))e(c(c(x))) → e(c(x))e(e(c(x))) → e(c(e(x)))c(c(c(c(x)))) → c(c(c(x)))) |
18.05
Statisticsiterations: 10 equalities (active): 200 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.011 time/maxk: 17.587 time/normalization: 0.189 time/overlaps: 0.106 time/orientation constraints: 2.287 time/project: 0 time/sat: 5.481 time/update context: 0.231 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr4
(RULES b(x) → d(d(x))d(d(d(d(e(x))))) → e(d(x))a(x) → d(d(d(d(x))))c(e(d(x))) → e(d(x))d(e(d(x))) → e(d(x))e(e(d(x))) → e(d(e(x)))e(d(d(x))) → e(d(x))e(d(c(x))) → e(d(x))e(c(x)) → e(d(x))d(d(d(c(x)))) → d(d(d(d(x))))c(d(x)) → d(d(d(d(x))))d(d(d(d(d(x))))) → d(d(d(d(x))))c(c(x)) → d(d(d(x)))) |
TPDB_thiemann27 | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ |
TPDB_zantema_z115 |
22.55
Statisticsiterations: 5 equalities (active): 120 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 2.324 time/maxk: 1.37 time/normalization: 8.109 time/overlaps: 1.609 time/orientation constraints: 0.927 time/project: 0 time/sat: 0.267 time/update context: 0.018 Convergent TRS(VAR x)
Completion of TPDB_zantema_z115
(RULES d(d(x)) → c(c(a(c(x))))d(c(c(c(x)))) → c(c(c(x)))c(d(x)) → d(c(x))d(c(c(a(c(x))))) → c(c(c(x)))c(c(c(a(x)))) → c(c(c(x)))d(c(a(c(x)))) → c(c(c(x)))d(c(c(a(d(x))))) → c(c(c(x)))d(c(a(d(x)))) → c(c(c(x)))c(c(c(c(x)))) → c(c(c(x)))a(c(c(x))) → c(c(c(x)))a(d(c(x))) → d(c(a(x)))a(a(x)) → d(c(x))b(x) → c(c(x))) |
384.84
Statisticsiterations: 16 equalities (active): 251 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.022 time/maxk: 384.306 time/normalization: 0.323 time/overlaps: 0.028 time/orientation constraints: 4.13 time/project: 0 time/sat: 366.487 time/update context: 0.395 Convergent TRS(VAR x)
Completion of TPDB_zantema_z115
(RULES d(d(x)) → c(c(a(c(x))))d(c(x)) → c(d(x))c(c(c(c(x)))) → c(c(c(x)))c(c(c(a(x)))) → c(c(c(x)))c(d(a(c(x)))) → c(c(c(x)))c(d(a(d(x)))) → c(c(c(x)))c(c(c(d(x)))) → c(c(c(x)))a(c(c(x))) → c(c(c(x)))a(c(d(x))) → c(d(a(x)))b(x) → c(c(x))a(a(x)) → c(d(x))) |
2.06
Statisticsiterations: 6 equalities (active): 96 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 1.924 time/normalization: 0.032 time/overlaps: 0.01 time/orientation constraints: 1.183 time/project: 0 time/sat: 0.307 time/update context: 0.01 Convergent TRS(VAR x)
Completion of TPDB_zantema_z115
(RULES a(c(c(x))) → c(c(c(x)))c(c(c(a(x)))) → c(c(c(x)))c(c(c(d(x)))) → c(c(c(x)))c(d(a(c(x)))) → c(c(c(x)))c(d(a(d(x)))) → c(c(c(x)))c(c(c(c(x)))) → c(c(c(x)))d(c(x)) → c(d(x))a(c(d(x))) → c(d(a(x)))d(d(x)) → c(c(a(c(x))))b(x) → c(c(x))a(a(x)) → c(d(x))) |
7.51
Statisticsiterations: 9 equalities (active): 164 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.014 time/maxk: 7.11 time/normalization: 0.185 time/overlaps: 0.063 time/orientation constraints: 1.792 time/project: 0 time/sat: 0.573 time/update context: 0.219 Convergent TRS(VAR x)
Completion of TPDB_zantema_z115
(RULES c(d(x)) → a(a(x))c(c(x)) → b(x)d(c(x)) → a(a(x))c(a(a(x))) → a(a(c(x)))a(a(c(a(c(x))))) → d(d(d(x)))d(a(a(x))) → d(d(d(x)))c(b(x)) → d(d(d(x)))b(a(a(x))) → d(d(d(x)))d(d(d(a(x)))) → d(d(d(x)))a(a(c(a(d(x))))) → d(d(d(x)))b(d(x)) → a(a(c(x)))a(a(a(c(x)))) → d(d(d(x)))a(a(a(a(x)))) → d(d(d(x)))a(a(d(x))) → d(d(d(x)))d(d(d(d(x)))) → d(d(d(x)))b(c(x)) → d(d(d(x)))a(d(d(x))) → d(d(d(x)))a(b(x)) → d(d(d(x)))d(b(x)) → a(a(c(x)))b(b(x)) → d(d(d(x)))b(a(c(x))) → d(d(x))) |
17.40
Statisticsiterations: 13 equalities (active): 190 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.021 time/maxk: 16.946 time/normalization: 0.171 time/overlaps: 0.141 time/orientation constraints: 4.054 time/project: 0 time/sat: 3.403 time/update context: 0.065 Convergent TRS(VAR x)
Completion of TPDB_zantema_z115
(RULES c(c(x)) → b(x)d(c(x)) → a(a(x))c(a(a(x))) → b(d(x))a(b(x)) → b(b(x))c(b(x)) → b(b(x))c(d(x)) → a(a(x))b(d(d(x))) → b(b(x))d(b(x)) → b(d(x))b(c(x)) → b(b(x))b(d(a(d(x)))) → b(b(x))d(d(d(x))) → b(b(x))a(a(d(x))) → b(b(x))a(a(a(a(x)))) → b(b(x))b(d(a(c(x)))) → b(b(x))a(d(d(x))) → b(b(x))b(a(a(x))) → b(b(x))d(a(a(x))) → b(b(x))b(b(d(x))) → b(b(x))b(b(b(x))) → b(b(x))b(b(a(x))) → b(b(x))a(a(c(x))) → b(d(x))b(a(c(x))) → d(d(x))) |
3.02
Statisticsiterations: 6 equalities (active): 98 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 2.853 time/normalization: 0.076 time/overlaps: 0.023 time/orientation constraints: 1.011 time/project: 0 time/sat: 0.394 time/update context: 0.037 Convergent TRS(VAR x)
Completion of TPDB_zantema_z115
(RULES c(d(x)) → a(a(x))d(c(x)) → a(a(x))c(a(a(x))) → a(a(c(x)))a(a(c(a(c(x))))) → c(c(c(x)))d(a(a(x))) → c(c(c(x)))c(c(c(a(x)))) → c(c(c(x)))a(a(c(a(d(x))))) → c(c(c(x)))a(a(d(x))) → c(c(c(x)))a(a(a(a(x)))) → c(c(c(x)))a(a(a(c(x)))) → c(c(c(x)))d(d(x)) → c(c(a(c(x))))a(c(c(x))) → c(c(c(x)))c(c(c(c(x)))) → c(c(c(x)))b(x) → c(c(x))) |
TPTP_BOO027-1_theory |
0.02
Statisticsiterations: 2 equalities (active): 9 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.012 time/normalization: 0 time/overlaps: 0.004 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR y x z)
Completion of TPTP_BOO027-1_theory
(RULES add(y,inverse(y)) → oneadd(multiply(y,inverse(y)),multiply(x,one)) → x,add(multiply(y,inverse(x)),multiply(x,add(y,inverse(x)))) → y,add(multiply(y,inverse(x)),multiply(y,add(y,inverse(x)))) → y,add(multiply(y,x),multiply(z,x)) → multiply(x,add(y,z))) |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.012 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.006 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR y x z)
Completion of TPTP_BOO027-1_theory
(RULES add(y,inverse(y)) → oneadd(multiply(y,inverse(y)),multiply(x,one)) → x,add(multiply(y,inverse(x)),multiply(x,add(y,inverse(x)))) → y,add(multiply(y,inverse(x)),multiply(y,add(y,inverse(x)))) → y,add(multiply(y,x),multiply(z,x)) → multiply(x,add(y,z))) |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.009 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR y x z)
Completion of TPTP_BOO027-1_theory
(RULES add(y,inverse(y)) → oneadd(multiply(y,inverse(y)),multiply(x,one)) → x,add(multiply(y,inverse(x)),multiply(x,add(y,inverse(x)))) → y,add(multiply(y,inverse(x)),multiply(y,add(y,inverse(x)))) → y,add(multiply(y,x),multiply(z,x)) → multiply(x,add(y,z))) |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.006 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR y x z)
Completion of TPTP_BOO027-1_theory
(RULES add(y,inverse(y)) → oneadd(multiply(y,inverse(y)),multiply(x,one)) → x,add(multiply(y,inverse(x)),multiply(x,add(y,inverse(x)))) → y,add(multiply(y,inverse(x)),multiply(y,add(y,inverse(x)))) → y,add(multiply(y,x),multiply(z,x)) → multiply(x,add(y,z))) |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.009 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR y x z)
Completion of TPTP_BOO027-1_theory
(RULES add(y,inverse(y)) → oneadd(multiply(y,inverse(y)),multiply(x,one)) → x,add(multiply(y,inverse(x)),multiply(x,add(y,inverse(x)))) → y,add(multiply(y,inverse(x)),multiply(y,add(y,inverse(x)))) → y,add(multiply(y,x),multiply(z,x)) → multiply(x,add(y,z))) |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.012 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.007 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR y x z)
Completion of TPTP_BOO027-1_theory
(RULES add(y,inverse(y)) → oneadd(multiply(y,inverse(y)),multiply(x,one)) → x,add(multiply(y,inverse(x)),multiply(x,add(y,inverse(x)))) → y,add(multiply(y,inverse(x)),multiply(y,add(y,inverse(x)))) → y,add(multiply(y,x),multiply(z,x)) → multiply(x,add(y,z))) |
TPTP_COL053-1_theory |
0.00
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y w)
Completion of TPTP_COL053-1_theory
(RULES response(compose(x,y),w) → response(x,response(y,w))) |
0.01
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y w)
Completion of TPTP_COL053-1_theory
(RULES response(compose(x,y),w) → response(x,response(y,w))) |
0.01
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y w)
Completion of TPTP_COL053-1_theory
(RULES response(compose(x,y),w) → response(x,response(y,w))) |
0.02
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.016 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.014 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y w)
Completion of TPTP_COL053-1_theory
(RULES response(compose(x,y),w) → response(x,response(y,w))) |
0.01
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y w)
Completion of TPTP_COL053-1_theory
(RULES response(compose(x,y),w) → response(x,response(y,w))) |
0.00
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.001 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y w)
Completion of TPTP_COL053-1_theory
(RULES response(compose(x,y),w) → response(x,response(y,w))) |
TPTP_COL056-1_theory |
0.02
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.012 time/normalization: 0.001 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y w)
Completion of TPTP_COL056-1_theory
(RULES response(a,c) → bresponse(a,b) → cresponse(compose(x,y),w) → response(x,response(y,w))) |
0.03
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.014 time/normalization: 0.001 time/overlaps: 0.002 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.004 time/update context: 0 Convergent TRS(VAR x y w)
Completion of TPTP_COL056-1_theory
(RULES response(a,c) → bresponse(a,b) → cresponse(compose(x,y),w) → response(x,response(y,w))) |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.002 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y w)
Completion of TPTP_COL056-1_theory
(RULES response(a,c) → bresponse(a,b) → cresponse(compose(x,y),w) → response(x,response(y,w))) |
0.02
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0.001 time/overlaps: 0.001 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y w)
Completion of TPTP_COL056-1_theory
(RULES response(a,c) → bresponse(a,b) → cresponse(compose(x,y),w) → response(x,response(y,w))) |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y w)
Completion of TPTP_COL056-1_theory
(RULES response(a,c) → bresponse(a,b) → cresponse(compose(x,y),w) → response(x,response(y,w))) |
0.04
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.017 time/normalization: 0.003 time/overlaps: 0.003 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.003 time/update context: 0 Convergent TRS(VAR x y w)
Completion of TPTP_COL056-1_theory
(RULES response(a,c) → bresponse(a,b) → cresponse(compose(x,y),w) → response(x,response(y,w))) |
TPTP_COL060-1_theory |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of TPTP_COL060-1_theory
(RULES apply(apply(apply(b,x),y),z) → apply(x,apply(y,z))apply(apply(t,x),y) → apply(y,x)) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of TPTP_COL060-1_theory
(RULES apply(apply(apply(b,x),y),z) → apply(x,apply(y,z))apply(apply(t,x),y) → apply(y,x)) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.004 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of TPTP_COL060-1_theory
(RULES apply(apply(apply(b,x),y),z) → apply(x,apply(y,z))apply(apply(t,x),y) → apply(y,x)) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.006 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of TPTP_COL060-1_theory
(RULES apply(apply(apply(b,x),y),z) → apply(x,apply(y,z))apply(apply(t,x),y) → apply(y,x)) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of TPTP_COL060-1_theory
(RULES apply(apply(apply(b,x),y),z) → apply(x,apply(y,z))apply(apply(t,x),y) → apply(y,x)) |
0.03
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.021 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.017 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y z)
Completion of TPTP_COL060-1_theory
(RULES apply(apply(apply(b,x),y),z) → apply(x,apply(y,z))apply(apply(t,x),y) → apply(y,x)) |
TPTP_COL085-1_theory |
0.00
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.001 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_COL085-1_theory
(RULES response(a,class="var">,b,class="var">),class="var">, → ,class="var">,b) |
0.00
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_COL085-1_theory
(RULES response(a,class="var">,b,class="var">),class="var">, → ,class="var">,b) |
0.00
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_COL085-1_theory
(RULES response(a,class="var">,b,class="var">),class="var">, → ,class="var">,b) |
0.00
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.001 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_COL085-1_theory
(RULES response(a,class="var">,b,class="var">),class="var">, → ,class="var">,b) |
0.01
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.004 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_COL085-1_theory
(RULES response(a,class="var">,b,class="var">),class="var">, → ,class="var">,b) |
0.01
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_COL085-1_theory
(RULES response(a,class="var">,b,class="var">),class="var">, → ,class="var">,b) |
TPTP_GRP010-4_theory | ∞ |
1.83
Statisticsiterations: 8 equalities (active): 111 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 1.616 time/normalization: 0.084 time/overlaps: 0.06 time/orientation constraints: 0.366 time/project: 0 time/sat: 0.267 time/update context: 0.066 Convergent TRS(VAR x y z)
Completion of TPTP_GRP010-4_theory
(RULES multiply(inverse(x),x) → identitymultiply(x,inverse(x)) → identityinverse(multiply(x,y)) → multiply(inverse(y),inverse(x))c → inverse(b)inverse(identity) → identityinverse(inverse(x)) → x,multiply(x,multiply(inverse(x),y)) → y,multiply(x,identity) → x,multiply(inverse(x),multiply(x,y)) → y,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))multiply(identity,x) → x,) |
4.22
Statisticsiterations: 12 equalities (active): 160 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.016 time/maxk: 2.852 time/normalization: 0.658 time/overlaps: 0.314 time/orientation constraints: 1.11 time/project: 0 time/sat: 0.223 time/update context: 0.045 Convergent TRS(VAR x y z)
Completion of TPTP_GRP010-4_theory
(RULES multiply(c,b) → identitymultiply(x,inverse(x)) → identityinverse(c) → bmultiply(inverse(x),x) → identityinverse(b) → cinverse(multiply(x,y)) → multiply(inverse(y),inverse(x))multiply(b,c) → identityinverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(b,multiply(c,x)) → x,multiply(x,multiply(inverse(x),y)) → y,multiply(c,multiply(b,x)) → x,multiply(inverse(x),multiply(x,y)) → y,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))multiply(identity,x) → x,) |
1.14
Statisticsiterations: 8 equalities (active): 95 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 0.879 time/normalization: 0.108 time/overlaps: 0.066 time/orientation constraints: 0.266 time/project: 0 time/sat: 0.058 time/update context: 0.058 Convergent TRS(VAR x y z)
Completion of TPTP_GRP010-4_theory
(RULES multiply(c,b) → identitymultiply(inverse(x),x) → identitymultiply(inverse(x),multiply(x,y)) → y,multiply(x,inverse(x)) → identitymultiply(b,c) → identityinverse(c) → binverse(b) → cmultiply(b,multiply(c,x)) → x,multiply(x,multiply(inverse(x),y)) → y,inverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(c,multiply(b,x)) → x,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))multiply(identity,x) → x,) |
9.40
Statisticsiterations: 12 equalities (active): 131 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.019 time/maxk: 8.861 time/normalization: 0.199 time/overlaps: 0.179 time/orientation constraints: 0.766 time/project: 0 time/sat: 2.33 time/update context: 0.055 Convergent TRS(VAR x y z)
Completion of TPTP_GRP010-4_theory
(RULES multiply(inverse(x),x) → identitymultiply(x,inverse(x)) → identityinverse(multiply(x,y)) → multiply(inverse(y),inverse(x))multiply(x,identity) → x,inverse(inverse(x)) → x,inverse(identity) → identitymultiply(x,multiply(inverse(x),y)) → y,b → inverse(c)multiply(inverse(x),multiply(x,y)) → y,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))multiply(identity,x) → x,) |
5.21
Statisticsiterations: 9 equalities (active): 116 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 4.939 time/normalization: 0.098 time/overlaps: 0.084 time/orientation constraints: 0.391 time/project: 0 time/sat: 0.844 time/update context: 0.083 Convergent TRS(VAR x y z)
Completion of TPTP_GRP010-4_theory
(RULES multiply(inverse(x),x) → identitymultiply(x,inverse(x)) → identityinverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(x,multiply(inverse(x),y)) → y,b → inverse(c)multiply(inverse(x),multiply(x,y)) → y,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))multiply(identity,x) → x,) |
TPTP_GRP011-4_theory | ∞ |
1.21
Statisticsiterations: 7 equalities (active): 86 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 0.891 time/normalization: 0.125 time/overlaps: 0.106 time/orientation constraints: 0.311 time/project: 0 time/sat: 0.091 time/update context: 0.055 Convergent TRS(VAR x y z)
Completion of TPTP_GRP011-4_theory
(RULES multiply(inverse(x),x) → identitymultiply(x,inverse(x)) → identityd → binverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))multiply(identity,x) → x,) |
4.61
Statisticsiterations: 10 equalities (active): 140 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.015 time/maxk: 3.195 time/normalization: 0.616 time/overlaps: 0.39 time/orientation constraints: 1.569 time/project: 0 time/sat: 0.157 time/update context: 0.051 Convergent TRS(VAR x y z)
Completion of TPTP_GRP011-4_theory
(RULES multiply(inverse(x),x) → identitymultiply(x,inverse(x)) → identityinverse(multiply(x,y)) → multiply(inverse(y),inverse(x))b → dinverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))multiply(identity,x) → x,) |
0.84
Statisticsiterations: 7 equalities (active): 90 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 0.547 time/normalization: 0.106 time/overlaps: 0.102 time/orientation constraints: 0.184 time/project: 0 time/sat: 0.032 time/update context: 0.041 Convergent TRS(VAR x y z)
Completion of TPTP_GRP011-4_theory
(RULES multiply(inverse(x),x) → identitymultiply(x,inverse(x)) → identityinverse(multiply(x,y)) → multiply(inverse(y),inverse(x))b → dinverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))multiply(identity,x) → x,) |
4.70
Statisticsiterations: 8 equalities (active): 103 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 4.338 time/normalization: 0.129 time/overlaps: 0.104 time/orientation constraints: 0.388 time/project: 0 time/sat: 1.096 time/update context: 0.021 Convergent TRS(VAR x y z)
Completion of TPTP_GRP011-4_theory
(RULES multiply(inverse(x),x) → identitymultiply(x,inverse(x)) → identityinverse(multiply(x,y)) → multiply(inverse(y),inverse(x))b → dinverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))multiply(identity,x) → x,) |
3.25
Statisticsiterations: 7 equalities (active): 93 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 2.944 time/normalization: 0.115 time/overlaps: 0.107 time/orientation constraints: 0.243 time/project: 0 time/sat: 0.579 time/update context: 0.065 Convergent TRS(VAR x y z)
Completion of TPTP_GRP011-4_theory
(RULES multiply(inverse(x),x) → identitymultiply(x,inverse(x)) → identityinverse(multiply(x,y)) → multiply(inverse(y),inverse(x))b → dinverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))multiply(identity,x) → x,) |
TPTP_GRP012-4_theory | ∞ |
0.22
Statisticsiterations: 4 equalities (active): 47 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.11 time/normalization: 0.031 time/overlaps: 0.053 time/orientation constraints: 0.055 time/project: 0 time/sat: 0.007 time/update context: 0.007 Convergent TRS(VAR x y z)
Completion of TPTP_GRP012-4_theory
(RULES inverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(inverse(x)) → x,inverse(identity) → identitymultiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(x,identity) → x,multiply(x,inverse(x)) → identitymultiply(identity,x) → x,multiply(inverse(x),x) → identitymultiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
1.14
Statisticsiterations: 6 equalities (active): 87 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.733 time/normalization: 0.136 time/overlaps: 0.157 time/orientation constraints: 0.524 time/project: 0 time/sat: 0.027 time/update context: 0.008 Convergent TRS(VAR x y z)
Completion of TPTP_GRP012-4_theory
(RULES inverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(inverse(x)) → x,inverse(identity) → identitymultiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(x,identity) → x,multiply(x,inverse(x)) → identitymultiply(identity,x) → x,multiply(inverse(x),x) → identitymultiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
0.19
Statisticsiterations: 4 equalities (active): 47 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.088 time/normalization: 0.037 time/overlaps: 0.04 time/orientation constraints: 0.046 time/project: 0 time/sat: 0.002 time/update context: 0.005 Convergent TRS(VAR x y z)
Completion of TPTP_GRP012-4_theory
(RULES inverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(inverse(x)) → x,inverse(identity) → identitymultiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(x,identity) → x,multiply(x,inverse(x)) → identitymultiply(identity,x) → x,multiply(inverse(x),x) → identitymultiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
0.48
Statisticsiterations: 4 equalities (active): 47 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.377 time/normalization: 0.029 time/overlaps: 0.049 time/orientation constraints: 0.076 time/project: 0 time/sat: 0.081 time/update context: 0.002 Convergent TRS(VAR x y z)
Completion of TPTP_GRP012-4_theory
(RULES inverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(inverse(x)) → x,inverse(identity) → identitymultiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(x,identity) → x,multiply(x,inverse(x)) → identitymultiply(identity,x) → x,multiply(inverse(x),x) → identitymultiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
0.43
Statisticsiterations: 4 equalities (active): 47 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.305 time/normalization: 0.051 time/overlaps: 0.04 time/orientation constraints: 0.063 time/project: 0 time/sat: 0.041 time/update context: 0.008 Convergent TRS(VAR x y z)
Completion of TPTP_GRP012-4_theory
(RULES inverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(inverse(x)) → x,inverse(identity) → identitymultiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(x,identity) → x,multiply(x,inverse(x)) → identitymultiply(identity,x) → x,multiply(inverse(x),x) → identitymultiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
TPTP_GRP393-2_theory |
0.01
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of TPTP_GRP393-2_theory
(RULES multiply(x,multiply(y,z)) → multiply(multiply(x,y),z)) |
0.00
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.001 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of TPTP_GRP393-2_theory
(RULES multiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
0.01
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of TPTP_GRP393-2_theory
(RULES multiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
0.00
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.001 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of TPTP_GRP393-2_theory
(RULES multiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
0.01
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of TPTP_GRP393-2_theory
(RULES multiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
0.00
Statisticsiterations: 1 equalities (active): 1 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.001 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of TPTP_GRP393-2_theory
(RULES multiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
TPTP_GRP394-3_theory | ∞ |
0.55
Statisticsiterations: 6 equalities (active): 67 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 0.366 time/normalization: 0.076 time/overlaps: 0.064 time/orientation constraints: 0.125 time/project: 0 time/sat: 0.02 time/update context: 0.036 Convergent TRS(VAR x y z)
Completion of TPTP_GRP394-3_theory
(RULES inverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(x,inverse(x)) → identitymultiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(identity,x) → x,multiply(inverse(x),x) → identitymultiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
2.98
Statisticsiterations: 9 equalities (active): 138 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 1.985 time/normalization: 0.461 time/overlaps: 0.3 time/orientation constraints: 1.098 time/project: 0 time/sat: 0.078 time/update context: 0.027 Convergent TRS(VAR x y z)
Completion of TPTP_GRP394-3_theory
(RULES inverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(x,inverse(x)) → identitymultiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(identity,x) → x,multiply(inverse(x),x) → identitymultiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
0.65
Statisticsiterations: 7 equalities (active): 76 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 0.36 time/normalization: 0.111 time/overlaps: 0.095 time/orientation constraints: 0.115 time/project: 0 time/sat: 0.012 time/update context: 0.03 Convergent TRS(VAR x y z)
Completion of TPTP_GRP394-3_theory
(RULES inverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(x,inverse(x)) → identitymultiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(identity,x) → x,multiply(inverse(x),x) → identitymultiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
1.85
Statisticsiterations: 6 equalities (active): 67 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 1.631 time/normalization: 0.075 time/overlaps: 0.074 time/orientation constraints: 0.165 time/project: 0 time/sat: 0.278 time/update context: 0.008 Convergent TRS(VAR x y z)
Completion of TPTP_GRP394-3_theory
(RULES inverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(x,inverse(x)) → identitymultiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(identity,x) → x,multiply(inverse(x),x) → identitymultiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
0.98
Statisticsiterations: 6 equalities (active): 63 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.845 time/normalization: 0.049 time/overlaps: 0.052 time/orientation constraints: 0.105 time/project: 0 time/sat: 0.059 time/update context: 0.021 Convergent TRS(VAR x y z)
Completion of TPTP_GRP394-3_theory
(RULES inverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(x,inverse(x)) → identitymultiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(identity,x) → x,multiply(inverse(x),x) → identitymultiply(multiply(x,y),z) → multiply(x,multiply(y,z))) |
TPTP_GRP454-1_theory | ∞ | ∞ | ∞ | ∞ |
103.68
Statisticsiterations: 15 equalities (active): 218 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.079 time/maxk: 102.253 time/normalization: 0.508 time/overlaps: 0.393 time/orientation constraints: 1.676 time/project: 0 time/sat: 75.378 time/update context: 0.142 Convergent TRS(VAR b a c)
Completion of TPTP_GRP454-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))multiply(inverse(b),multiply(b,a)) → a,multiply(b,multiply(inverse(b),a)) → a,inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(b,inverse(b)) → identitymultiply(b,identity) → b,multiply(identity,b) → b,multiply(inverse(b),b) → identityinverse(inverse(b)) → b,inverse(identity) → identity) |
54.25
Statisticsiterations: 15 equalities (active): 240 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.048 time/maxk: 53.021 time/normalization: 0.605 time/overlaps: 0.297 time/orientation constraints: 1.401 time/project: 0 time/sat: 20.269 time/update context: 0.966 Convergent TRS(VAR b a c)
Completion of TPTP_GRP454-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(b,multiply(inverse(b),a)) → a,multiply(b,identity) → b,multiply(b,inverse(b)) → identitymultiply(inverse(b),multiply(b,a)) → a,multiply(identity,b) → b,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
TPTP_GRP457-1_theory | ∞ | ∞ | ∞ |
12.28
Statisticsiterations: 13 equalities (active): 229 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.044 time/maxk: 11.095 time/normalization: 0.476 time/overlaps: 0.356 time/orientation constraints: 1.612 time/project: 0 time/sat: 0.38 time/update context: 0.615 Convergent TRS(VAR b a c)
Completion of TPTP_GRP457-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(b,identity) → b,multiply(b,inverse(b)) → identitymultiply(inverse(b),multiply(b,a)) → a,multiply(b,multiply(inverse(b),a)) → a,inverse(inverse(b)) → b,multiply(identity,b) → b,inverse(identity) → identitymultiply(inverse(b),b) → identity) |
67.47
Statisticsiterations: 14 equalities (active): 224 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.064 time/maxk: 66.542 time/normalization: 0.3 time/overlaps: 0.355 time/orientation constraints: 1.281 time/project: 0 time/sat: 47.116 time/update context: 0.102 Convergent TRS(VAR b a c)
Completion of TPTP_GRP457-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))multiply(inverse(b),multiply(b,a)) → a,multiply(b,multiply(inverse(b),a)) → a,inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(b,identity) → b,multiply(b,inverse(b)) → identitymultiply(identity,b) → b,multiply(inverse(b),b) → identityinverse(inverse(b)) → b,inverse(identity) → identity) |
91.37
Statisticsiterations: 16 equalities (active): 254 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.07 time/maxk: 89.203 time/normalization: 1.212 time/overlaps: 0.36 time/orientation constraints: 1.842 time/project: 0 time/sat: 29.014 time/update context: 1.757 Convergent TRS(VAR b a c)
Completion of TPTP_GRP457-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(b,inverse(b)) → identitymultiply(inverse(b),multiply(b,a)) → a,multiply(b,multiply(inverse(b),a)) → a,multiply(b,identity) → b,multiply(identity,b) → b,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
TPTP_GRP460-1_theory | ∞ |
8.30
Statisticsiterations: 12 equalities (active): 164 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.035 time/maxk: 7.554 time/normalization: 0.354 time/overlaps: 0.19 time/orientation constraints: 0.827 time/project: 0 time/sat: 2.998 time/update context: 0.273 Convergent TRS(VAR b a c)
Completion of TPTP_GRP460-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))multiply(identity,b) → b,inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(inverse(b),multiply(b,a)) → a,multiply(b,inverse(b)) → identitymultiply(b,multiply(inverse(b),a)) → a,multiply(b,identity) → b,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
∞ |
102.09
Statisticsiterations: 34 equalities (active): 327 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.23 time/maxk: 65.087 time/normalization: 29.11 time/overlaps: 2.917 time/orientation constraints: 4.839 time/project: 0 time/sat: 0.895 time/update context: 4.694 Convergent TRS(VAR b a c)
Completion of TPTP_GRP460-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))multiply(inverse(b),multiply(b,a)) → a,inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(b,inverse(b)) → identitymultiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(inverse(b)) → b,multiply(identity,b) → b,multiply(b,identity) → b,multiply(b,multiply(inverse(b),a)) → a,inverse(identity) → identitymultiply(inverse(b),b) → identity) |
214.95
Statisticsiterations: 19 equalities (active): 276 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.073 time/maxk: 212.989 time/normalization: 0.802 time/overlaps: 0.459 time/orientation constraints: 2.815 time/project: 0 time/sat: 162.842 time/update context: 0.26 Convergent TRS(VAR b a c)
Completion of TPTP_GRP460-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(inverse(b),multiply(b,a)) → a,multiply(identity,b) → b,multiply(b,inverse(b)) → identitymultiply(b,identity) → b,multiply(inverse(b),b) → identityinverse(inverse(b)) → b,multiply(b,multiply(inverse(b),a)) → a,inverse(identity) → identity) |
120.36
Statisticsiterations: 18 equalities (active): 286 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.078 time/maxk: 118.134 time/normalization: 0.951 time/overlaps: 0.724 time/orientation constraints: 1.833 time/project: 0 time/sat: 47.54 time/update context: 1.761 Convergent TRS(VAR b a c)
Completion of TPTP_GRP460-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(inverse(b),multiply(b,a)) → a,multiply(identity,b) → b,multiply(b,inverse(b)) → identitymultiply(b,multiply(inverse(b),a)) → a,multiply(b,identity) → b,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
TPTP_GRP463-1_theory | ∞ |
10.42
Statisticsiterations: 12 equalities (active): 178 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.025 time/maxk: 9.703 time/normalization: 0.397 time/overlaps: 0.128 time/orientation constraints: 0.864 time/project: 0 time/sat: 2.667 time/update context: 0.376 Convergent TRS(VAR b a c)
Completion of TPTP_GRP463-1_theory
(RULES multiply(identity,b) → b,divide(b,a) → multiply(b,inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))inverse(inverse(b)) → b,multiply(b,inverse(b)) → identitymultiply(inverse(b),multiply(b,a)) → a,multiply(b,identity) → b,multiply(b,multiply(inverse(b),a)) → a,inverse(identity) → identitymultiply(inverse(b),b) → identity) |
∞ |
120.35
Statisticsiterations: 25 equalities (active): 414 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.166 time/maxk: 109.214 time/normalization: 5.318 time/overlaps: 2.349 time/orientation constraints: 6.038 time/project: 0 time/sat: 1.746 time/update context: 6.413 Convergent TRS(VAR b a c)
Completion of TPTP_GRP463-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(inverse(b),multiply(b,a)) → a,multiply(identity,b) → b,multiply(b,inverse(b)) → identitymultiply(b,identity) → b,multiply(b,multiply(inverse(b),a)) → a,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
357.14
Statisticsiterations: 22 equalities (active): 308 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.09 time/maxk: 353.592 time/normalization: 1.608 time/overlaps: 0.922 time/orientation constraints: 4.607 time/project: 0 time/sat: 265.513 time/update context: 0.349 Convergent TRS(VAR b a c)
Completion of TPTP_GRP463-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(inverse(b),multiply(b,a)) → a,multiply(identity,b) → b,multiply(b,inverse(b)) → identitymultiply(b,identity) → b,multiply(inverse(b),b) → identityinverse(inverse(b)) → b,multiply(b,multiply(inverse(b),a)) → a,inverse(identity) → identity) |
71.93
Statisticsiterations: 16 equalities (active): 241 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.053 time/maxk: 70.133 time/normalization: 0.872 time/overlaps: 0.382 time/orientation constraints: 1.491 time/project: 0 time/sat: 23.644 time/update context: 1.11 Convergent TRS(VAR b a c)
Completion of TPTP_GRP463-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(identity,b) → b,multiply(b,inverse(b)) → identitymultiply(inverse(b),multiply(b,a)) → a,multiply(b,identity) → b,multiply(b,multiply(inverse(b),a)) → a,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
TPTP_GRP481-1_theory | ∞ | ∞ | ∞ |
36.23
Statisticsiterations: 17 equalities (active): 276 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.07 time/maxk: 34.273 time/normalization: 0.983 time/overlaps: 0.424 time/orientation constraints: 2.445 time/project: 0 time/sat: 0.828 time/update context: 2.031 Convergent TRS(VAR c a b)
Completion of TPTP_GRP481-1_theory
(RULES multiply(identity,c,lass="var">c) → c,double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,multiply(c,lass="var">c,identity) → c,multiply(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(inverse(c,lass="var">c),c,lass="var">c) → identityinverse(inverse(c,lass="var">c)) → c,inverse(identity) → identitymultiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,) |
53.99
Statisticsiterations: 15 equalities (active): 226 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.052 time/maxk: 53.16 time/normalization: 0.318 time/overlaps: 0.211 time/orientation constraints: 2.608 time/project: 0 time/sat: 33.248 time/update context: 0.171 Convergent TRS(VAR c a b)
Completion of TPTP_GRP481-1_theory
(RULES double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))multiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(c,lass="var">c,identity) → c,multiply(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(inverse(c,lass="var">c),c,lass="var">c) → identityinverse(identity) → identitymultiply(identity,c,lass="var">c) → c,inverse(inverse(c,lass="var">c)) → c,) |
∞ |
TPTP_GRP484-1_theory | ∞ |
71.65
Statisticsiterations: 20 equalities (active): 261 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.169 time/maxk: 68.801 time/normalization: 1.522 time/overlaps: 0.548 time/orientation constraints: 4.143 time/project: 0 time/sat: 26.603 time/update context: 2.343 Convergent TRS(VAR c a b)
Completion of TPTP_GRP484-1_theory
(RULES multiply(identity,c,lass="var">c) → c,double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,multiply(c,lass="var">c,identity) → c,multiply(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(inverse(c,lass="var">c),c,lass="var">c) → identityinverse(identity) → identityinverse(inverse(c,lass="var">c)) → c,) |
∞ |
383.06
Statisticsiterations: 64 equalities (active): 480 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.411 time/maxk: 321.186 time/normalization: 32.157 time/overlaps: 8.934 time/orientation constraints: 26.444 time/project: 0 time/sat: 8.038 time/update context: 17.955 Convergent TRS(VAR c a b)
Completion of TPTP_GRP484-1_theory
(RULES double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,multiply(identity,c,lass="var">c) → c,multiply(c,lass="var">c,identity) → c,multiply(inverse(c,lass="var">c),c,lass="var">c) → identitymultiply(c,lass="var">c,inverse(c,lass="var">c)) → identityinverse(inverse(c,lass="var">c)) → c,inverse(identity) → identity) |
156.46
Statisticsiterations: 20 equalities (active): 275 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.104 time/maxk: 152.94 time/normalization: 1.727 time/overlaps: 0.816 time/orientation constraints: 6.179 time/project: 0 time/sat: 77.115 time/update context: 0.311 Convergent TRS(VAR c a b)
Completion of TPTP_GRP484-1_theory
(RULES double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))multiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(c,lass="var">c,identity) → c,multiply(inverse(c,lass="var">c),c,lass="var">c) → identitymultiply(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(identity,c,lass="var">c) → c,inverse(identity) → identityinverse(inverse(c,lass="var">c)) → c,) |
157.11
Statisticsiterations: 18 equalities (active): 279 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.061 time/maxk: 154.053 time/normalization: 1.566 time/overlaps: 0.603 time/orientation constraints: 4.196 time/project: 0 time/sat: 70.331 time/update context: 1.64 Convergent TRS(VAR c a b)
Completion of TPTP_GRP484-1_theory
(RULES double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,multiply(c,lass="var">c,identity) → c,multiply(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,multiply(identity,c,lass="var">c) → c,multiply(inverse(c,lass="var">c),c,lass="var">c) → identityinverse(identity) → identityinverse(inverse(c,lass="var">c)) → c,) |
TPTP_GRP487-1_theory | ∞ |
54.04
Statisticsiterations: 19 equalities (active): 279 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.136 time/maxk: 51.291 time/normalization: 1.49 time/overlaps: 0.463 time/orientation constraints: 3.768 time/project: 0 time/sat: 16.94 time/update context: 2.079 Convergent TRS(VAR c a b)
Completion of TPTP_GRP487-1_theory
(RULES multiply(inverse(c,lass="var">c),c,lass="var">c) → identitymultiply(c,lass="var">c,identity) → c,double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))multiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(identity,c,lass="var">c) → c,inverse(inverse(c,lass="var">c)) → c,multiply(c,lass="var">c,inverse(c,lass="var">c)) → identityinverse(identity) → identity) |
∞ | ∞ | ∞ |
172.83
Statisticsiterations: 20 equalities (active): 288 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.103 time/maxk: 170.563 time/normalization: 1.179 time/overlaps: 0.398 time/orientation constraints: 3.903 time/project: 0 time/sat: 58.77 time/update context: 2.379 Convergent TRS(VAR c a b)
Completion of TPTP_GRP487-1_theory
(RULES double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))multiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(identity,c,lass="var">c) → c,multiply(c,lass="var">c,identity) → c,multiply(c,lass="var">c,inverse(c,lass="var">c)) → identityinverse(inverse(c,lass="var">c)) → c,multiply(inverse(c,lass="var">c),c,lass="var">c) → identityinverse(identity) → identity) |
TPTP_GRP490-1_theory | ∞ |
51.04
Statisticsiterations: 19 equalities (active): 279 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.182 time/maxk: 48.477 time/normalization: 1.174 time/overlaps: 0.546 time/orientation constraints: 3.354 time/project: 0 time/sat: 6.975 time/update context: 2.807 Convergent TRS(VAR c a b)
Completion of TPTP_GRP490-1_theory
(RULES double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))multiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(identity,c,lass="var">c) → c,multiply(c,lass="var">c,identity) → c,multiply(inverse(c,lass="var">c),c,lass="var">c) → identitymultiply(c,lass="var">c,inverse(c,lass="var">c)) → identityinverse(identity) → identityinverse(inverse(c,lass="var">c)) → c,) |
∞ |
229.60
Statisticsiterations: 53 equalities (active): 360 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.284 time/maxk: 203.66 time/normalization: 12.335 time/overlaps: 7.345 time/orientation constraints: 16.082 time/project: 0 time/sat: 6.442 time/update context: 10.427 Convergent TRS(VAR c a b)
Completion of TPTP_GRP490-1_theory
(RULES double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))multiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,multiply(inverse(c,lass="var">c),c,lass="var">c) → identityinverse(inverse(c,lass="var">c)) → c,inverse(identity) → identitymultiply(identity,c,lass="var">c) → c,multiply(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(c,lass="var">c,identity) → c,) |
∞ |
195.31
Statisticsiterations: 20 equalities (active): 299 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.083 time/maxk: 191.995 time/normalization: 1.575 time/overlaps: 0.834 time/orientation constraints: 3.275 time/project: 0 time/sat: 104.66 time/update context: 1.668 Convergent TRS(VAR c a b)
Completion of TPTP_GRP490-1_theory
(RULES double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))multiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,multiply(inverse(c,lass="var">c),c,lass="var">c) → identityinverse(identity) → identitymultiply(identity,c,lass="var">c) → c,multiply(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(c,lass="var">c,identity) → c,inverse(inverse(c,lass="var">c)) → c,) |
TPTP_GRP493-1_theory | ∞ |
17.16
Statisticsiterations: 13 equalities (active): 191 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.126 time/maxk: 15.744 time/normalization: 0.656 time/overlaps: 0.293 time/orientation constraints: 1.704 time/project: 0 time/sat: 2.273 time/update context: 1.017 Convergent TRS(VAR b a c)
Completion of TPTP_GRP493-1_theory
(RULES double_divide(b,a) → multiply(inverse(b),inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(b,multiply(inverse(b),a)) → a,multiply(b,identity) → b,multiply(identity,b) → b,multiply(b,inverse(b)) → identitymultiply(inverse(b),b) → identitymultiply(inverse(b),multiply(b,a)) → a,inverse(inverse(b)) → b,inverse(identity) → identity) |
12.55
Statisticsiterations: 19 equalities (active): 274 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.078 time/maxk: 10.367 time/normalization: 0.894 time/overlaps: 0.65 time/orientation constraints: 3.28 time/project: 0 time/sat: 0.539 time/update context: 0.175 Convergent TRS(VAR b a c)
Completion of TPTP_GRP493-1_theory
(RULES double_divide(b,a) → multiply(inverse(b),inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))multiply(b,multiply(inverse(b),a)) → a,inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(b,inverse(b)) → identitymultiply(inverse(b),b) → identitymultiply(inverse(b),multiply(b,a)) → a,inverse(identity) → identitymultiply(identity,b) → b,multiply(b,identity) → b,inverse(inverse(b)) → b,) |
∞ |
39.01
Statisticsiterations: 14 equalities (active): 192 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.124 time/maxk: 37.752 time/normalization: 0.466 time/overlaps: 0.271 time/orientation constraints: 1.668 time/project: 0 time/sat: 9.889 time/update context: 0.119 Convergent TRS(VAR b a c)
Completion of TPTP_GRP493-1_theory
(RULES double_divide(b,a) → multiply(inverse(b),inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(b,multiply(inverse(b),a)) → a,multiply(b,identity) → b,multiply(identity,b) → b,multiply(inverse(b),b) → identitymultiply(b,inverse(b)) → identitymultiply(inverse(b),multiply(b,a)) → a,inverse(identity) → identityinverse(inverse(b)) → b,) |
187.19
Statisticsiterations: 22 equalities (active): 314 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.131 time/maxk: 183.691 time/normalization: 1.66 time/overlaps: 0.814 time/orientation constraints: 4.091 time/project: 0 time/sat: 44.183 time/update context: 2.628 Convergent TRS(VAR b a c)
Completion of TPTP_GRP493-1_theory
(RULES double_divide(b,a) → multiply(inverse(b),inverse(a))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(b,identity) → b,multiply(identity,b) → b,multiply(b,multiply(inverse(b),a)) → a,multiply(b,inverse(b)) → identitymultiply(inverse(b),b) → identitymultiply(inverse(b),multiply(b,a)) → a,inverse(identity) → identityinverse(inverse(b)) → b,) |
TPTP_GRP496-1_theory | ∞ |
18.28
Statisticsiterations: 14 equalities (active): 210 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.053 time/maxk: 17.284 time/normalization: 0.483 time/overlaps: 0.24 time/orientation constraints: 1.834 time/project: 0 time/sat: 4.234 time/update context: 0.713 Convergent TRS(VAR c a b)
Completion of TPTP_GRP496-1_theory
(RULES double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(inverse(c,lass="var">c),c,lass="var">c) → identitymultiply(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,multiply(c,lass="var">c,identity) → c,multiply(identity,c,lass="var">c) → c,inverse(identity) → identityinverse(inverse(c,lass="var">c)) → c,) |
∞ | ∞ |
35.01
Statisticsiterations: 14 equalities (active): 190 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.042 time/maxk: 34.379 time/normalization: 0.225 time/overlaps: 0.219 time/orientation constraints: 1.632 time/project: 0 time/sat: 19.983 time/update context: 0.089 Convergent TRS(VAR c a b)
Completion of TPTP_GRP496-1_theory
(RULES double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(c,lass="var">c,identity) → c,multiply(identity,c,lass="var">c) → c,multiply(inverse(c,lass="var">c),c,lass="var">c) → identitymultiply(c,lass="var">c,inverse(c,lass="var">c)) → identityinverse(identity) → identityinverse(inverse(c,lass="var">c)) → c,) |
∞ |
TPTP_HWC004-1_theory |
0.02
Statisticsiterations: 1 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.011 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_HWC004-1_theory
(RULES and(n1,class="var">,n1,class="var">),class="var">, → ,class="var">,n1and(n0,class="var">,n0,class="var">),class="var">, → ,class="var">,n0and(n0,class="var">,n1,class="var">),class="var">, → ,class="var">,n0and(n1,class="var">,n0,class="var">),class="var">, → ,class="var">,n0or(n0,class="var">,n0,class="var">),class="var">, → ,class="var">,n0or(n0,class="var">,n1,class="var">),class="var">, → ,class="var">,n1or(n1,class="var">,n0,class="var">),class="var">, → ,class="var">,n1or(n1,class="var">,n1,class="var">),class="var">, → ,class="var">,n1not(n0,class="var">),class="var">, → ,class="var">,n1not(n1,class="var">),class="var">, → ,class="var">,n0) |
0.03
Statisticsiterations: 1 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.019 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.012 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_HWC004-1_theory
(RULES and(n1,class="var">,n1,class="var">),class="var">, → ,class="var">,n1and(n0,class="var">,n0,class="var">),class="var">, → ,class="var">,n0and(n0,class="var">,n1,class="var">),class="var">, → ,class="var">,n0and(n1,class="var">,n0,class="var">),class="var">, → ,class="var">,n0or(n0,class="var">,n0,class="var">),class="var">, → ,class="var">,n0or(n0,class="var">,n1,class="var">),class="var">, → ,class="var">,n1or(n1,class="var">,n0,class="var">),class="var">, → ,class="var">,n1or(n1,class="var">,n1,class="var">),class="var">, → ,class="var">,n1not(n0,class="var">),class="var">, → ,class="var">,n1not(n1,class="var">),class="var">, → ,class="var">,n0) |
0.02
Statisticsiterations: 1 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.015 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.012 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_HWC004-1_theory
(RULES and(n1,class="var">,n1,class="var">),class="var">, → ,class="var">,n1and(n0,class="var">,n0,class="var">),class="var">, → ,class="var">,n0and(n0,class="var">,n1,class="var">),class="var">, → ,class="var">,n0and(n1,class="var">,n0,class="var">),class="var">, → ,class="var">,n0or(n0,class="var">,n0,class="var">),class="var">, → ,class="var">,n0or(n0,class="var">,n1,class="var">),class="var">, → ,class="var">,n1or(n1,class="var">,n0,class="var">),class="var">, → ,class="var">,n1or(n1,class="var">,n1,class="var">),class="var">, → ,class="var">,n1not(n0,class="var">),class="var">, → ,class="var">,n1not(n1,class="var">),class="var">, → ,class="var">,n0) |
0.02
Statisticsiterations: 1 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.01 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_HWC004-1_theory
(RULES and(n1,class="var">,n1,class="var">),class="var">, → ,class="var">,n1and(n0,class="var">,n0,class="var">),class="var">, → ,class="var">,n0and(n0,class="var">,n1,class="var">),class="var">, → ,class="var">,n0and(n1,class="var">,n0,class="var">),class="var">, → ,class="var">,n0or(n0,class="var">,n0,class="var">),class="var">, → ,class="var">,n0or(n0,class="var">,n1,class="var">),class="var">, → ,class="var">,n1or(n1,class="var">,n0,class="var">),class="var">, → ,class="var">,n1or(n1,class="var">,n1,class="var">),class="var">, → ,class="var">,n1not(n0,class="var">),class="var">, → ,class="var">,n1not(n1,class="var">),class="var">, → ,class="var">,n0) |
0.03
Statisticsiterations: 1 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.022 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_HWC004-1_theory
(RULES and(n1,class="var">,n1,class="var">),class="var">, → ,class="var">,n1and(n0,class="var">,n0,class="var">),class="var">, → ,class="var">,n0and(n0,class="var">,n1,class="var">),class="var">, → ,class="var">,n0and(n1,class="var">,n0,class="var">),class="var">, → ,class="var">,n0or(n0,class="var">,n0,class="var">),class="var">, → ,class="var">,n0or(n0,class="var">,n1,class="var">),class="var">, → ,class="var">,n1or(n1,class="var">,n0,class="var">),class="var">, → ,class="var">,n1or(n1,class="var">,n1,class="var">),class="var">, → ,class="var">,n1not(n0,class="var">),class="var">, → ,class="var">,n1not(n1,class="var">),class="var">, → ,class="var">,n0) |
0.01
Statisticsiterations: 1 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_HWC004-1_theory
(RULES and(n1,class="var">,n1,class="var">),class="var">, → ,class="var">,n1and(n0,class="var">,n0,class="var">),class="var">, → ,class="var">,n0and(n0,class="var">,n1,class="var">),class="var">, → ,class="var">,n0and(n1,class="var">,n0,class="var">),class="var">, → ,class="var">,n0or(n0,class="var">,n0,class="var">),class="var">, → ,class="var">,n0or(n0,class="var">,n1,class="var">),class="var">, → ,class="var">,n1or(n1,class="var">,n0,class="var">),class="var">, → ,class="var">,n1or(n1,class="var">,n1,class="var">),class="var">, → ,class="var">,n1not(n0,class="var">),class="var">, → ,class="var">,n1not(n1,class="var">),class="var">, → ,class="var">,n0) |
TPTP_HWC004-2_theory |
0.02
Statisticsiterations: 1 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.017 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.001 time/update context: 0.006 Convergent TRS(VAR x)
Completion of TPTP_HWC004-2_theory
(RULES and(x,n0) → n0and(x,n1) → x,or(x,n0) → x,or(x,n1) → n1not(n0) → n1not(n1) → n0) |
0.02
Statisticsiterations: 1 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.015 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.003 time/project: 0 time/sat: 0.008 time/update context: 0 Convergent TRS(VAR x)
Completion of TPTP_HWC004-2_theory
(RULES and(x,n0) → n0and(x,n1) → x,or(x,n0) → x,or(x,n1) → n1not(n0) → n1not(n1) → n0) |
0.01
Statisticsiterations: 1 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of TPTP_HWC004-2_theory
(RULES and(x,n0) → n0and(x,n1) → x,or(x,n0) → x,or(x,n1) → n1not(n0) → n1not(n1) → n0) |
0.02
Statisticsiterations: 1 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of TPTP_HWC004-2_theory
(RULES and(x,n0) → n0and(x,n1) → x,or(x,n0) → x,or(x,n1) → n1not(n0) → n1not(n1) → n0) |
0.01
Statisticsiterations: 1 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of TPTP_HWC004-2_theory
(RULES and(x,n0) → n0and(x,n1) → x,or(x,n0) → x,or(x,n1) → n1not(n0) → n1not(n1) → n0) |
0.01
Statisticsiterations: 1 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of TPTP_HWC004-2_theory
(RULES and(x,n0) → n0and(x,n1) → x,or(x,n0) → x,or(x,n1) → n1not(n0) → n1not(n1) → n0) |
TPTP_SWV262-2_theory |
0.02
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.014 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR vg vh vy ta)
Completion of TPTP_SWV262-2_theory
(RULES c_union(c_insert(vg,vh,vy),ta,vy) → c_insert(vg,c_union(vh,ta,vy),vy)c_union(c_Message_Oparts(vg),c_Message_Oparts(vh),tc_Message_Omsg) → c_Message_Oparts(c_union(vg,vh,tc_Message_Omsg))c_union(c_emptyset,vg,vh) → vg,) |
0.04
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.033 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.03 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR vg vh vy ta)
Completion of TPTP_SWV262-2_theory
(RULES c_union(c_insert(vg,vh,vy),ta,vy) → c_insert(vg,c_union(vh,ta,vy),vy)c_union(c_Message_Oparts(vg),c_Message_Oparts(vh),tc_Message_Omsg) → c_Message_Oparts(c_union(vg,vh,tc_Message_Omsg))c_union(c_emptyset,vg,vh) → vg,) |
0.03
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.016 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR vg vh vy ta)
Completion of TPTP_SWV262-2_theory
(RULES c_union(c_insert(vg,vh,vy),ta,vy) → c_insert(vg,c_union(vh,ta,vy),vy)c_union(c_Message_Oparts(vg),c_Message_Oparts(vh),tc_Message_Omsg) → c_Message_Oparts(c_union(vg,vh,tc_Message_Omsg))c_union(c_emptyset,vg,vh) → vg,) |
0.02
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.014 time/normalization: 0 time/overlaps: 0.003 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR vg vh vy ta)
Completion of TPTP_SWV262-2_theory
(RULES c_union(c_insert(vg,vh,vy),ta,vy) → c_insert(vg,c_union(vh,ta,vy),vy)c_union(c_Message_Oparts(vg),c_Message_Oparts(vh),tc_Message_Omsg) → c_Message_Oparts(c_union(vg,vh,tc_Message_Omsg))c_union(c_emptyset,vg,vh) → vg,) |
0.04
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.026 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.021 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR vg vh vy ta)
Completion of TPTP_SWV262-2_theory
(RULES c_union(c_insert(vg,vh,vy),ta,vy) → c_insert(vg,c_union(vh,ta,vy),vy)c_union(c_Message_Oparts(vg),c_Message_Oparts(vh),tc_Message_Omsg) → c_Message_Oparts(c_union(vg,vh,tc_Message_Omsg))c_union(c_emptyset,vg,vh) → vg,) |
0.03
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.015 time/normalization: 0 time/overlaps: 0.005 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR vg vh vy ta)
Completion of TPTP_SWV262-2_theory
(RULES c_union(c_insert(vg,vh,vy),ta,vy) → c_insert(vg,c_union(vh,ta,vy),vy)c_union(c_Message_Oparts(vg),c_Message_Oparts(vh),tc_Message_Omsg) → c_Message_Oparts(c_union(vg,vh,tc_Message_Omsg))c_union(c_emptyset,vg,vh) → vg,) |
WS06_proofreduction |
7.54
Statisticsiterations: 6 equalities (active): 139 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.015 time/maxk: 1.881 time/normalization: 1.627 time/overlaps: 2.072 time/orientation constraints: 1.36 time/project: 0 time/sat: 0.299 time/update context: 0.022 Convergent TRS(VAR x y z)
Completion of WS06_proofreduction
(RULES trans(CongrNot(x),CongrNot(y)) → CongrNot(trans(x,y))trans(CongrAnd1(x),AndTrue2) → trans(AndTrue2,x)trans(CongrAnd2(x),AndTrue1) → trans(AndTrue1,x)trans(CongrOr1(x),OrFalse2) → trans(OrFalse2,x)trans(CongrOr2(x),OrFalse1) → trans(OrFalse1,x)trans(CongrAnd2(x),AndFalse1) → AndFalse1trans(CongrAnd1(x),AndFalse2) → AndFalse2trans(CongrOr2(x),OrTrue1) → OrTrue1trans(CongrOr1(x),OrTrue2) → OrTrue2trans(CongrOr1(x),trans(OrFalse2,y)) → trans(OrFalse2,trans(x,y))trans(CongrNot(x),trans(CongrNot(y),z)) → trans(CongrNot(trans(x,y)),z)trans(CongrOr2(x),trans(OrFalse1,y)) → trans(OrFalse1,trans(x,y))trans(CongrAnd2(x),trans(AndTrue1,y)) → trans(AndTrue1,trans(x,y))trans(CongrAnd1(x),trans(AndTrue2,y)) → trans(AndTrue2,trans(x,y))trans(CongrOr1(x),trans(OrTrue2,y)) → trans(OrTrue2,y)trans(CongrOr2(x),trans(OrTrue1,y)) → trans(OrTrue1,y)trans(CongrAnd1(x),trans(AndFalse2,y)) → trans(AndFalse2,y)trans(CongrAnd2(x),trans(AndFalse1,y)) → trans(AndFalse1,y)trans(CongrAnd2(x),CongrAnd2(y)) → CongrAnd2(trans(x,y))trans(CongrAnd1(x),CongrAnd1(y)) → CongrAnd1(trans(x,y))trans(CongrAnd1(x),trans(CongrAnd1(y),z)) → trans(CongrAnd1(trans(x,y)),z)trans(CongrAnd2(x),trans(CongrAnd2(y),z)) → trans(CongrAnd2(trans(x,y)),z)trans(CongrAnd1(x),trans(CongrAnd2(y),AndTrue2)) → trans(CongrAnd2(y),trans(AndTrue2,x))trans(CongrAnd1(x),trans(CongrAnd2(y),AndFalse2)) → trans(CongrAnd2(y),AndFalse2)trans(CongrOr2(x),CongrOr2(y)) → CongrOr2(trans(x,y))trans(CongrOr1(x),CongrOr1(y)) → CongrOr1(trans(x,y))trans(CongrOr1(x),trans(CongrOr2(y),OrFalse2)) → trans(CongrOr2(y),trans(OrFalse2,x))trans(CongrOr1(x),trans(CongrOr2(y),OrTrue2)) → trans(CongrOr2(y),OrTrue2)trans(CongrAnd1(x),trans(CongrAnd2(y),trans(AndTrue2,z))) → trans(CongrAnd2(y),trans(AndTrue2,trans(x,z)))trans(CongrAnd1(x),trans(CongrAnd2(y),trans(AndFalse2,z))) → trans(CongrAnd2(y),trans(AndFalse2,z))trans(CongrOr1(x),trans(CongrOr1(y),z)) → trans(CongrOr1(trans(x,y)),z)trans(CongrOr2(x),trans(CongrOr2(y),z)) → trans(CongrOr2(trans(x,y)),z)trans(CongrOr1(x),trans(CongrOr2(y),trans(OrFalse2,z))) → trans(CongrOr2(y),trans(OrFalse2,trans(x,z)))trans(CongrOr1(x),trans(CongrOr2(y),trans(OrTrue2,z))) → trans(CongrOr2(y),trans(OrTrue2,z))trans(CongrOr2(x),trans(CongrOr1(y),z)) → trans(CongrOr1(y),trans(CongrOr2(x),z))trans(CongrOr2(x),CongrOr1(y)) → trans(CongrOr1(y),CongrOr2(x))trans(CongrAnd2(x),trans(CongrAnd1(y),z)) → trans(CongrAnd1(y),trans(CongrAnd2(x),z))trans(CongrAnd2(x),CongrAnd1(y)) → trans(CongrAnd1(y),CongrAnd2(x))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(x,refl) → x,CongrOr1(refl) → reflCongrOr2(refl) → reflCongrAnd1(refl) → reflCongrAnd2(refl) → reflCongrNot(refl) → refl) |
20.57
Statisticsiterations: 11 equalities (active): 198 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.032 time/maxk: 18.273 time/normalization: 0.857 time/overlaps: 0.525 time/orientation constraints: 4.291 time/project: 0 time/sat: 8.392 time/update context: 0.702 Convergent TRS(VAR x y z)
Completion of WS06_proofreduction
(RULES trans(CongrNot(x),CongrNot(y)) → CongrNot(trans(x,y))trans(CongrAnd1(x),AndTrue2) → trans(AndTrue2,x)trans(CongrAnd2(x),AndTrue1) → trans(AndTrue1,x)trans(CongrOr1(x),OrFalse2) → trans(OrFalse2,x)trans(CongrOr2(x),OrFalse1) → trans(OrFalse1,x)trans(CongrAnd2(x),AndFalse1) → AndFalse1trans(CongrAnd1(x),AndFalse2) → AndFalse2trans(CongrOr2(x),OrTrue1) → OrTrue1trans(CongrOr1(x),OrTrue2) → OrTrue2trans(x,trans(y,z)) → trans(trans(x,y),z)trans(trans(x,CongrOr2(y)),OrFalse1) → trans(trans(x,OrFalse1),y)trans(trans(x,CongrOr1(y)),OrFalse2) → trans(trans(x,OrFalse2),y)trans(trans(x,CongrAnd2(y)),AndTrue1) → trans(trans(x,AndTrue1),y)trans(trans(x,CongrAnd1(y)),AndTrue2) → trans(trans(x,AndTrue2),y)trans(CongrAnd2(x),CongrAnd2(y)) → CongrAnd2(trans(x,y))trans(CongrAnd1(x),CongrAnd1(y)) → CongrAnd1(trans(x,y))trans(CongrOr1(x),CongrOr1(y)) → CongrOr1(trans(x,y))trans(CongrOr2(x),CongrOr2(y)) → CongrOr2(trans(x,y))trans(trans(CongrAnd1(x),CongrAnd2(y)),AndTrue2) → trans(trans(CongrAnd2(y),AndTrue2),x)trans(trans(CongrAnd1(x),CongrAnd2(y)),AndFalse2) → trans(CongrAnd2(y),AndFalse2)trans(trans(CongrOr1(x),CongrOr2(y)),OrFalse2) → trans(trans(CongrOr2(y),OrFalse2),x)trans(trans(CongrOr1(x),CongrOr2(y)),OrTrue2) → trans(CongrOr2(y),OrTrue2)trans(trans(trans(x,CongrOr1(y)),CongrOr2(z)),OrTrue2) → trans(trans(x,CongrOr2(z)),OrTrue2)trans(trans(trans(x,CongrOr1(y)),CongrOr2(z)),OrFalse2) → trans(trans(trans(x,CongrOr2(z)),OrFalse2),y)trans(trans(x,CongrOr1(y)),CongrOr1(z)) → trans(x,CongrOr1(trans(y,z)))trans(trans(x,CongrOr2(y)),CongrOr2(z)) → trans(x,CongrOr2(trans(y,z)))trans(trans(x,CongrOr2(y)),CongrOr1(z)) → trans(trans(x,CongrOr1(z)),CongrOr2(y))trans(trans(trans(x,CongrAnd1(y)),CongrAnd2(z)),AndFalse2) → trans(trans(x,CongrAnd2(z)),AndFalse2)trans(trans(trans(x,CongrAnd1(y)),CongrAnd2(z)),AndTrue2) → trans(trans(trans(x,CongrAnd2(z)),AndTrue2),y)trans(CongrOr2(x),CongrOr1(y)) → trans(CongrOr1(y),CongrOr2(x))trans(trans(x,CongrAnd2(y)),CongrAnd2(z)) → trans(x,CongrAnd2(trans(y,z)))trans(trans(x,CongrAnd1(y)),CongrAnd1(z)) → trans(x,CongrAnd1(trans(y,z)))trans(trans(x,CongrAnd2(y)),CongrAnd1(z)) → trans(trans(x,CongrAnd1(z)),CongrAnd2(y))trans(CongrAnd2(x),CongrAnd1(y)) → trans(CongrAnd1(y),CongrAnd2(x))trans(trans(x,CongrAnd2(y)),AndFalse1) → trans(x,AndFalse1)trans(trans(x,CongrAnd1(y)),AndFalse2) → trans(x,AndFalse2)trans(trans(x,CongrOr2(y)),OrTrue1) → trans(x,OrTrue1)trans(trans(x,CongrOr1(y)),OrTrue2) → trans(x,OrTrue2)trans(trans(x,CongrNot(y)),CongrNot(z)) → trans(x,CongrNot(trans(y,z)))trans(refl,x) → x,trans(x,refl) → x,CongrOr1(refl) → reflCongrOr2(refl) → reflCongrAnd1(refl) → reflCongrAnd2(refl) → reflCongrNot(refl) → refl) |
9.80
Statisticsiterations: 9 equalities (active): 185 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.022 time/maxk: 7.916 time/normalization: 0.627 time/overlaps: 0.626 time/orientation constraints: 4.472 time/project: 0 time/sat: 0.853 time/update context: 0.09 Convergent TRS(VAR x y z)
Completion of WS06_proofreduction
(RULES trans(CongrNot(x),CongrNot(y)) → CongrNot(trans(x,y))trans(CongrAnd1(x),AndTrue2) → trans(AndTrue2,x)trans(CongrAnd2(x),AndTrue1) → trans(AndTrue1,x)trans(CongrOr1(x),OrFalse2) → trans(OrFalse2,x)trans(CongrOr2(x),OrFalse1) → trans(OrFalse1,x)trans(CongrAnd2(x),AndFalse1) → AndFalse1trans(CongrAnd1(x),AndFalse2) → AndFalse2trans(CongrOr2(x),OrTrue1) → OrTrue1trans(CongrOr1(x),OrTrue2) → OrTrue2trans(CongrOr1(x),trans(OrFalse2,y)) → trans(OrFalse2,trans(x,y))trans(CongrAnd1(x),trans(AndTrue2,y)) → trans(AndTrue2,trans(x,y))trans(CongrNot(x),trans(CongrNot(y),z)) → trans(CongrNot(trans(x,y)),z)trans(CongrOr2(x),trans(OrFalse1,y)) → trans(OrFalse1,trans(x,y))trans(CongrAnd2(x),trans(AndTrue1,y)) → trans(AndTrue1,trans(x,y))trans(CongrOr1(x),trans(OrTrue2,y)) → trans(OrTrue2,y)trans(CongrOr2(x),trans(OrTrue1,y)) → trans(OrTrue1,y)trans(CongrAnd1(x),trans(AndFalse2,y)) → trans(AndFalse2,y)trans(CongrAnd2(x),trans(AndFalse1,y)) → trans(AndFalse1,y)trans(CongrOr1(x),CongrOr2(y)) → trans(CongrOr2(y),CongrOr1(x))trans(CongrAnd2(x),CongrAnd2(y)) → CongrAnd2(trans(x,y))trans(CongrAnd1(x),CongrAnd1(y)) → CongrAnd1(trans(x,y))trans(CongrOr2(x),CongrOr2(y)) → CongrOr2(trans(x,y))trans(CongrOr1(x),CongrOr1(y)) → CongrOr1(trans(x,y))trans(CongrAnd1(x),trans(CongrAnd2(y),AndFalse2)) → trans(CongrAnd2(y),AndFalse2)trans(CongrOr1(x),trans(CongrOr2(y),z)) → trans(CongrOr2(y),trans(CongrOr1(x),z))trans(CongrOr1(x),trans(CongrOr1(y),z)) → trans(CongrOr1(trans(x,y)),z)trans(CongrOr2(x),trans(CongrOr2(y),z)) → trans(CongrOr2(trans(x,y)),z)trans(CongrAnd1(x),trans(CongrAnd1(y),z)) → trans(CongrAnd1(trans(x,y)),z)trans(CongrAnd2(x),trans(CongrAnd2(y),z)) → trans(CongrAnd2(trans(x,y)),z)trans(CongrAnd1(x),trans(CongrAnd2(y),trans(AndTrue2,z))) → trans(CongrAnd2(y),trans(AndTrue2,trans(x,z)))trans(CongrAnd1(x),trans(CongrAnd2(y),trans(AndFalse2,z))) → trans(CongrAnd2(y),trans(AndFalse2,z))trans(CongrAnd1(x),trans(CongrAnd2(y),AndTrue2)) → trans(CongrAnd2(y),trans(AndTrue2,x))trans(CongrOr2(x),trans(CongrOr1(y),trans(OrTrue1,z))) → trans(CongrOr1(y),trans(OrTrue1,z))trans(CongrOr2(x),trans(CongrOr1(y),trans(OrFalse1,z))) → trans(CongrOr1(y),trans(OrFalse1,trans(x,z)))trans(CongrOr2(x),trans(CongrOr1(y),OrTrue1)) → trans(CongrOr1(y),OrTrue1)trans(CongrOr2(x),trans(CongrOr1(y),OrFalse1)) → trans(CongrOr1(y),trans(OrFalse1,x))trans(CongrAnd2(x),trans(CongrAnd1(y),z)) → trans(CongrAnd1(y),trans(CongrAnd2(x),z))trans(CongrAnd2(x),CongrAnd1(y)) → trans(CongrAnd1(y),CongrAnd2(x))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(x,refl) → x,CongrOr1(refl) → reflCongrOr2(refl) → reflCongrAnd1(refl) → reflCongrAnd2(refl) → reflCongrNot(refl) → refl) |
3.43
Statisticsiterations: 6 equalities (active): 138 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 2.53 time/normalization: 0.262 time/overlaps: 0.369 time/orientation constraints: 1.305 time/project: 0 time/sat: 0.2 time/update context: 0.109 Convergent TRS(VAR x y z)
Completion of WS06_proofreduction
(RULES trans(CongrNot(x),CongrNot(y)) → CongrNot(trans(x,y))trans(CongrAnd1(x),AndTrue2) → trans(AndTrue2,x)trans(CongrAnd2(x),AndTrue1) → trans(AndTrue1,x)trans(CongrOr1(x),OrFalse2) → trans(OrFalse2,x)trans(CongrOr2(x),OrFalse1) → trans(OrFalse1,x)trans(CongrAnd2(x),AndFalse1) → AndFalse1trans(CongrAnd1(x),AndFalse2) → AndFalse2trans(CongrOr2(x),OrTrue1) → OrTrue1trans(CongrOr1(x),OrTrue2) → OrTrue2trans(CongrOr1(x),trans(OrFalse2,y)) → trans(OrFalse2,trans(x,y))trans(CongrNot(x),trans(CongrNot(y),z)) → trans(CongrNot(trans(x,y)),z)trans(CongrAnd1(x),trans(AndTrue2,y)) → trans(AndTrue2,trans(x,y))trans(CongrOr2(x),trans(OrFalse1,y)) → trans(OrFalse1,trans(x,y))trans(CongrAnd2(x),trans(AndTrue1,y)) → trans(AndTrue1,trans(x,y))trans(CongrOr1(x),trans(OrTrue2,y)) → trans(OrTrue2,y)trans(CongrOr2(x),trans(OrTrue1,y)) → trans(OrTrue1,y)trans(CongrAnd1(x),trans(AndFalse2,y)) → trans(AndFalse2,y)trans(CongrAnd2(x),trans(AndFalse1,y)) → trans(AndFalse1,y)trans(CongrAnd1(x),CongrAnd1(y)) → CongrAnd1(trans(x,y))trans(CongrAnd2(x),CongrAnd2(y)) → CongrAnd2(trans(x,y))trans(CongrAnd1(x),trans(CongrAnd1(y),z)) → trans(CongrAnd1(trans(x,y)),z)trans(CongrAnd2(x),trans(CongrAnd2(y),z)) → trans(CongrAnd2(trans(x,y)),z)trans(CongrOr1(x),CongrOr2(y)) → trans(CongrOr2(y),CongrOr1(x))trans(CongrOr2(x),CongrOr2(y)) → CongrOr2(trans(x,y))trans(CongrOr1(x),CongrOr1(y)) → CongrOr1(trans(x,y))trans(CongrOr1(x),trans(CongrOr2(y),z)) → trans(CongrOr2(y),trans(CongrOr1(x),z))trans(CongrOr1(x),trans(CongrOr1(y),z)) → trans(CongrOr1(trans(x,y)),z)trans(CongrOr2(x),trans(CongrOr2(y),z)) → trans(CongrOr2(trans(x,y)),z)trans(CongrAnd1(x),trans(CongrAnd2(y),trans(AndTrue2,z))) → trans(CongrAnd2(y),trans(AndTrue2,trans(x,z)))trans(CongrAnd1(x),trans(CongrAnd2(y),trans(AndFalse2,z))) → trans(CongrAnd2(y),trans(AndFalse2,z))trans(CongrAnd1(x),trans(CongrAnd2(y),AndTrue2)) → trans(CongrAnd2(y),trans(AndTrue2,x))trans(CongrAnd1(x),trans(CongrAnd2(y),AndFalse2)) → trans(CongrAnd2(y),AndFalse2)trans(CongrOr2(x),trans(CongrOr1(y),OrTrue1)) → trans(CongrOr1(y),OrTrue1)trans(CongrOr2(x),trans(CongrOr1(y),OrFalse1)) → trans(CongrOr1(y),trans(OrFalse1,x))trans(CongrOr2(x),trans(CongrOr1(y),trans(OrTrue1,z))) → trans(CongrOr1(y),trans(OrTrue1,z))trans(CongrOr2(x),trans(CongrOr1(y),trans(OrFalse1,z))) → trans(CongrOr1(y),trans(OrFalse1,trans(x,z)))trans(CongrAnd2(x),trans(CongrAnd1(y),z)) → trans(CongrAnd1(y),trans(CongrAnd2(x),z))trans(CongrAnd2(x),CongrAnd1(y)) → trans(CongrAnd1(y),CongrAnd2(x))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(x,refl) → x,CongrOr1(refl) → reflCongrOr2(refl) → reflCongrAnd1(refl) → reflCongrAnd2(refl) → reflCongrNot(refl) → refl) |
9.22
Statisticsiterations: 6 equalities (active): 133 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.014 time/maxk: 7.691 time/normalization: 0.467 time/overlaps: 0.638 time/orientation constraints: 2.165 time/project: 0 time/sat: 2.612 time/update context: 0.037 Convergent TRS(VAR x y z)
Completion of WS06_proofreduction
(RULES trans(CongrNot(x),CongrNot(y)) → CongrNot(trans(x,y))trans(CongrAnd1(x),AndTrue2) → trans(AndTrue2,x)trans(CongrAnd2(x),AndTrue1) → trans(AndTrue1,x)trans(CongrOr1(x),OrFalse2) → trans(OrFalse2,x)trans(CongrOr2(x),OrFalse1) → trans(OrFalse1,x)trans(CongrAnd2(x),AndFalse1) → AndFalse1trans(CongrAnd1(x),AndFalse2) → AndFalse2trans(CongrOr2(x),OrTrue1) → OrTrue1trans(CongrOr1(x),OrTrue2) → OrTrue2trans(x,trans(y,z)) → trans(trans(x,y),z)trans(trans(x,CongrOr2(y)),OrFalse1) → trans(trans(x,OrFalse1),y)trans(trans(x,CongrOr1(y)),OrFalse2) → trans(trans(x,OrFalse2),y)trans(trans(x,CongrAnd2(y)),AndTrue1) → trans(trans(x,AndTrue1),y)trans(trans(x,CongrAnd1(y)),AndTrue2) → trans(trans(x,AndTrue2),y)trans(CongrAnd1(x),CongrAnd2(y)) → trans(CongrAnd2(y),CongrAnd1(x))trans(CongrOr1(x),CongrOr2(y)) → trans(CongrOr2(y),CongrOr1(x))trans(CongrOr2(x),CongrOr2(y)) → CongrOr2(trans(x,y))trans(CongrAnd2(x),CongrAnd2(y)) → CongrAnd2(trans(x,y))trans(CongrAnd1(x),CongrAnd1(y)) → CongrAnd1(trans(x,y))trans(CongrOr1(x),CongrOr1(y)) → CongrOr1(trans(x,y))trans(trans(x,CongrOr1(y)),CongrOr2(z)) → trans(trans(x,CongrOr2(z)),CongrOr1(y))trans(trans(x,CongrAnd1(y)),CongrAnd2(z)) → trans(trans(x,CongrAnd2(z)),CongrAnd1(y))trans(trans(CongrOr2(x),CongrOr1(y)),OrTrue1) → trans(CongrOr1(y),OrTrue1)trans(trans(CongrAnd2(x),CongrAnd1(y)),AndFalse1) → trans(CongrAnd1(y),AndFalse1)trans(trans(trans(x,CongrAnd2(y)),CongrAnd1(z)),AndTrue1) → trans(trans(trans(x,CongrAnd1(z)),AndTrue1),y)trans(trans(trans(x,CongrOr2(y)),CongrOr1(z)),OrFalse1) → trans(trans(trans(x,CongrOr1(z)),OrFalse1),y)trans(trans(trans(x,CongrOr2(y)),CongrOr1(z)),OrTrue1) → trans(trans(x,CongrOr1(z)),OrTrue1)trans(trans(trans(x,CongrAnd2(y)),CongrAnd1(z)),AndFalse1) → trans(trans(x,CongrAnd1(z)),AndFalse1)trans(trans(x,CongrOr2(y)),CongrOr2(z)) → trans(x,CongrOr2(trans(y,z)))trans(trans(x,CongrAnd2(y)),CongrAnd2(z)) → trans(x,CongrAnd2(trans(y,z)))trans(trans(x,CongrAnd1(y)),CongrAnd1(z)) → trans(x,CongrAnd1(trans(y,z)))trans(trans(x,CongrOr1(y)),CongrOr1(z)) → trans(x,CongrOr1(trans(y,z)))trans(trans(CongrOr2(x),CongrOr1(y)),OrFalse1) → trans(trans(CongrOr1(y),OrFalse1),x)trans(trans(CongrAnd2(x),CongrAnd1(y)),AndTrue1) → trans(trans(CongrAnd1(y),AndTrue1),x)trans(trans(x,CongrAnd2(y)),AndFalse1) → trans(x,AndFalse1)trans(trans(x,CongrAnd1(y)),AndFalse2) → trans(x,AndFalse2)trans(trans(x,CongrOr2(y)),OrTrue1) → trans(x,OrTrue1)trans(trans(x,CongrOr1(y)),OrTrue2) → trans(x,OrTrue2)trans(trans(x,CongrNot(y)),CongrNot(z)) → trans(x,CongrNot(trans(y,z)))trans(refl,x) → x,trans(x,refl) → x,CongrOr1(refl) → reflCongrOr2(refl) → reflCongrAnd1(refl) → reflCongrAnd2(refl) → reflCongrNot(refl) → refl) |
5.16
Statisticsiterations: 6 equalities (active): 124 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 4.281 time/normalization: 0.242 time/overlaps: 0.27 time/orientation constraints: 1.272 time/project: 0 time/sat: 0.984 time/update context: 0.092 Convergent TRS(VAR x y z)
Completion of WS06_proofreduction
(RULES trans(CongrNot(x),CongrNot(y)) → CongrNot(trans(x,y))trans(CongrAnd1(x),AndTrue2) → trans(AndTrue2,x)trans(CongrAnd2(x),AndTrue1) → trans(AndTrue1,x)trans(CongrOr1(x),OrFalse2) → trans(OrFalse2,x)trans(CongrOr2(x),OrFalse1) → trans(OrFalse1,x)trans(CongrAnd2(x),AndFalse1) → AndFalse1trans(CongrAnd1(x),AndFalse2) → AndFalse2trans(CongrOr2(x),OrTrue1) → OrTrue1trans(CongrOr1(x),OrTrue2) → OrTrue2trans(CongrOr1(x),trans(OrFalse2,y)) → trans(OrFalse2,trans(x,y))trans(CongrNot(x),trans(CongrNot(y),z)) → trans(CongrNot(trans(x,y)),z)trans(CongrAnd1(x),trans(AndTrue2,y)) → trans(AndTrue2,trans(x,y))trans(CongrOr2(x),trans(OrFalse1,y)) → trans(OrFalse1,trans(x,y))trans(CongrAnd2(x),trans(AndTrue1,y)) → trans(AndTrue1,trans(x,y))trans(CongrOr1(x),trans(OrTrue2,y)) → trans(OrTrue2,y)trans(CongrOr2(x),trans(OrTrue1,y)) → trans(OrTrue1,y)trans(CongrAnd1(x),trans(AndFalse2,y)) → trans(AndFalse2,y)trans(CongrAnd2(x),trans(AndFalse1,y)) → trans(AndFalse1,y)trans(CongrAnd2(x),CongrAnd2(y)) → CongrAnd2(trans(x,y))trans(CongrAnd1(x),CongrAnd1(y)) → CongrAnd1(trans(x,y))trans(CongrAnd1(x),trans(CongrAnd1(y),z)) → trans(CongrAnd1(trans(x,y)),z)trans(CongrAnd2(x),trans(CongrAnd2(y),z)) → trans(CongrAnd2(trans(x,y)),z)trans(CongrOr1(x),CongrOr2(y)) → trans(CongrOr2(y),CongrOr1(x))trans(CongrOr2(x),CongrOr2(y)) → CongrOr2(trans(x,y))trans(CongrOr1(x),CongrOr1(y)) → CongrOr1(trans(x,y))trans(CongrOr1(x),trans(CongrOr2(y),z)) → trans(CongrOr2(y),trans(CongrOr1(x),z))trans(CongrOr1(x),trans(CongrOr1(y),z)) → trans(CongrOr1(trans(x,y)),z)trans(CongrOr2(x),trans(CongrOr2(y),z)) → trans(CongrOr2(trans(x,y)),z)trans(CongrAnd1(x),trans(CongrAnd2(y),trans(AndTrue2,z))) → trans(CongrAnd2(y),trans(AndTrue2,trans(x,z)))trans(CongrAnd1(x),trans(CongrAnd2(y),trans(AndFalse2,z))) → trans(CongrAnd2(y),trans(AndFalse2,z))trans(CongrAnd1(x),trans(CongrAnd2(y),AndTrue2)) → trans(CongrAnd2(y),trans(AndTrue2,x))trans(CongrAnd1(x),trans(CongrAnd2(y),AndFalse2)) → trans(CongrAnd2(y),AndFalse2)trans(CongrOr2(x),trans(CongrOr1(y),OrTrue1)) → trans(CongrOr1(y),OrTrue1)trans(CongrOr2(x),trans(CongrOr1(y),OrFalse1)) → trans(CongrOr1(y),trans(OrFalse1,x))trans(CongrOr2(x),trans(CongrOr1(y),trans(OrTrue1,z))) → trans(CongrOr1(y),trans(OrTrue1,z))trans(CongrOr2(x),trans(CongrOr1(y),trans(OrFalse1,z))) → trans(CongrOr1(y),trans(OrFalse1,trans(x,z)))trans(CongrAnd2(x),trans(CongrAnd1(y),z)) → trans(CongrAnd1(y),trans(CongrAnd2(x),z))trans(CongrAnd2(x),CongrAnd1(y)) → trans(CongrAnd1(y),CongrAnd2(x))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(x,refl) → x,CongrOr1(refl) → reflCongrOr2(refl) → reflCongrAnd1(refl) → reflCongrAnd2(refl) → reflCongrNot(refl) → refl) |
aufgabe3_2 |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.006 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_2
(RULES g(x) → f(f(x))) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_2
(RULES g(f(x)) → f(g(x))f(f(x)) → g(x)) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_2
(RULES g(f(x)) → f(g(x))f(f(x)) → g(x)) |
0.00
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_2
(RULES g(f(x)) → f(g(x))f(f(x)) → g(x)) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.006 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_2
(RULES g(f(x)) → f(g(x))f(f(x)) → g(x)) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_2
(RULES g(f(x)) → f(g(x))f(f(x)) → g(x)) |
aufgabe3_3 |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_3
(RULES f(x) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_3
(RULES f(x) → x,) |
0.01
Statisticsiterations: 3 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_3
(RULES f(x) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_3
(RULES f(x) → x,) |
0.01
Statisticsiterations: 3 equalities (active): 4 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_3
(RULES f(x) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_3
(RULES f(x) → x,) |
fggx |
0.01
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.003 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of fggx
(RULES f(x) → g(g(x))g(g(g(x))) → x,) |
0.02
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x)
Completion of fggx
(RULES g(g(x)) → f(x)g(f(x)) → x,f(f(x)) → g(x)f(g(x)) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.006 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of fggx
(RULES g(g(x)) → f(x)g(f(x)) → x,f(f(x)) → g(x)f(g(x)) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.006 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x)
Completion of fggx
(RULES g(g(x)) → f(x)g(f(x)) → x,f(f(x)) → g(x)f(g(x)) → x,) |
0.01
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.006 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x)
Completion of fggx
(RULES g(g(x)) → f(x)g(f(x)) → x,f(f(x)) → g(x)f(g(x)) → x,) |
0.02
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.015 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.007 time/project: 0 time/sat: 0.003 time/update context: 0 Convergent TRS(VAR x)
Completion of fggx
(RULES g(g(x)) → f(x)g(f(x)) → x,f(f(x)) → g(x)f(g(x)) → x,) |
fib | ∞ |
0.55
Statisticsiterations: 2 equalities (active): 37 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.508 time/normalization: 0.007 time/overlaps: 0.008 time/orientation constraints: 0.179 time/project: 0 time/sat: 0.29 time/update context: 0.003 Convergent TRS(VAR x y)
Completion of fib
(RULES p(x,y) → u(b(x,y))u(b(x,0)) → x,u(b(x,s(y))) → s(u(b(x,y)))n(b(x,y)) → b(u(b(x,y)),x)f(0) → 0f(s(0)) → s(0)f(s(s(x))) → u(b(f(s(x)),f(x)))g(x) → b(f(s(x)),f(x))) |
7.95
Statisticsiterations: 11 equalities (active): 135 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 7.555 time/normalization: 0.104 time/overlaps: 0.062 time/orientation constraints: 4.106 time/project: 0 time/sat: 1.807 time/update context: 0.037 Convergent TRS(VAR x y)
Completion of fib
(RULES p(x,y) → u(b(x,y))f(s(s(x))) → u(b(f(s(x)),f(x)))g(x) → b(f(s(x)),f(x))u(b(x,0)) → x,u(b(x,s(y))) → s(u(b(x,y)))n(b(x,y)) → b(u(b(x,y)),x)f(0) → 0f(s(0)) → s(0)) |
∞ |
0.16
Statisticsiterations: 2 equalities (active): 26 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.142 time/normalization: 0.002 time/overlaps: 0.004 time/orientation constraints: 0.065 time/project: 0 time/sat: 0.061 time/update context: 0 Convergent TRS(VAR x y)
Completion of fib
(RULES p(x,s(y)) → s(p(x,y))f(s(s(x))) → p(f(s(x)),f(x))p(x,0) → x,f(0) → 0f(s(0)) → s(0)n(b(x,y)) → b(p(x,y),x)u(b(x,y)) → p(x,y)g(x) → b(f(s(x)),f(x))) |
3.65
Statisticsiterations: 7 equalities (active): 101 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 3.508 time/normalization: 0.027 time/overlaps: 0.025 time/orientation constraints: 1.207 time/project: 0 time/sat: 1.312 time/update context: 0.036 Convergent TRS(VAR x y)
Completion of fib
(RULES p(x,s(y)) → s(p(x,y))p(x,0) → x,f(0) → 0f(s(0)) → s(0)f(s(s(x))) → p(f(s(x)),f(x))n(b(x,y)) → b(p(x,y),x)u(b(x,y)) → p(x,y)g(x) → b(f(s(x)),f(x))) |
lr_theory | ∞ |
1.66
Statisticsiterations: 8 equalities (active): 97 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 1.397 time/normalization: 0.128 time/overlaps: 0.065 time/orientation constraints: 0.596 time/project: 0 time/sat: 0.269 time/update context: 0.055 Convergent TRS(VAR x y z)
Completion of lr_theory
(RULES f(x,i(x)) → ef(x,e) → i(i(x))i(f(x,y)) → f(i(y),i(x))i(i(i(x))) → i(x)f(i(x),f(x,y)) → y,f(i(i(x)),y) → f(x,y)i(e) → ef(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(e,x) → x,) |
12.28
Statisticsiterations: 16 equalities (active): 198 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.04 time/maxk: 7.134 time/normalization: 2.61 time/overlaps: 0.906 time/orientation constraints: 3.636 time/project: 0 time/sat: 0.703 time/update context: 0.089 Convergent TRS(VAR x y z)
Completion of lr_theory
(RULES f(x,i(x)) → ef(i(x),e) → i(x)i(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,i(i(x)) → f(x,e)i(e) → ef(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(e,x) → x,) |
3.15
Statisticsiterations: 9 equalities (active): 121 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 2.234 time/normalization: 0.425 time/overlaps: 0.271 time/orientation constraints: 0.671 time/project: 0 time/sat: 0.063 time/update context: 0.165 Convergent TRS(VAR x y z)
Completion of lr_theory
(RULES f(x,i(x)) → ef(i(x),e) → i(x)i(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,i(i(x)) → f(x,e)i(e) → ef(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(e,x) → x,) |
5.88
Statisticsiterations: 8 equalities (active): 101 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.014 time/maxk: 5.167 time/normalization: 0.317 time/overlaps: 0.218 time/orientation constraints: 0.677 time/project: 0 time/sat: 0.421 time/update context: 0.016 Convergent TRS(VAR x y z)
Completion of lr_theory
(RULES f(x,i(x)) → ef(i(x),e) → i(x)i(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,i(i(x)) → f(x,e)i(e) → ef(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(e,x) → x,) |
4.47
Statisticsiterations: 8 equalities (active): 107 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 4.033 time/normalization: 0.216 time/overlaps: 0.116 time/orientation constraints: 0.573 time/project: 0 time/sat: 0.126 time/update context: 0.109 Convergent TRS(VAR x y z)
Completion of lr_theory
(RULES f(x,i(x)) → ef(i(x),e) → i(x)i(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,i(i(x)) → f(x,e)i(e) → ef(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(e,x) → x,) |
rl_theory | ∞ |
3.04
Statisticsiterations: 9 equalities (active): 112 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 2.673 time/normalization: 0.172 time/overlaps: 0.097 time/orientation constraints: 0.906 time/project: 0 time/sat: 0.691 time/update context: 0.086 Convergent TRS(VAR x y z)
Completion of rl_theory
(RULES f(i(x),x) → ef(x,f(e,y)) → f(x,y)f(e,f(i(x),y)) → f(i(x),y)f(e,i(x)) → i(x)i(f(x,y)) → f(i(y),i(x))f(x,f(y,i(y))) → x,f(x,f(y,f(i(y),z))) → f(x,z)i(i(x)) → f(e,x)i(e) → ef(i(x),f(x,y)) → f(e,y)f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
256.67
Statisticsiterations: 67 equalities (active): 247 equalities (passive): 0 restarts: 3 time/cache: 0 time/set ops: 0.745 time/maxk: 42.812 time/normalization: 125.744 time/overlaps: 13.189 time/orientation constraints: 21.133 time/project: 0 time/sat: 1.755 time/update context: 0.436 Convergent TRS(VAR x y z)
Completion of rl_theory
(RULES f(i(x),x) → ef(x,f(e,y)) → f(x,y)f(e,i(x)) → i(x)f(e,f(i(x),y)) → f(i(x),y)f(x,f(y,f(i(y),z))) → f(x,z)f(x,f(y,i(y))) → x,i(f(x,y)) → f(i(y),i(x))i(i(x)) → f(e,x)i(e) → ef(i(x),f(x,y)) → f(e,y)f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
47.43
Statisticsiterations: 17 equalities (active): 230 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.123 time/maxk: 21.308 time/normalization: 16.17 time/overlaps: 2.252 time/orientation constraints: 3.912 time/project: 0 time/sat: 0.31 time/update context: 2.202 Convergent TRS(VAR x y z)
Completion of rl_theory
(RULES f(i(x),x) → ef(x,f(e,y)) → f(x,y)f(e,f(i(x),y)) → f(i(x),y)f(e,i(x)) → i(x)i(f(x,y)) → f(i(y),i(x))f(x,f(y,f(i(y),z))) → f(x,z)f(x,f(y,i(y))) → x,i(i(x)) → f(e,x)i(e) → ef(i(x),f(x,y)) → f(e,y)f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
10.20
Statisticsiterations: 10 equalities (active): 121 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.01 time/maxk: 9.148 time/normalization: 0.499 time/overlaps: 0.258 time/orientation constraints: 1.064 time/project: 0 time/sat: 1.655 time/update context: 0.031 Convergent TRS(VAR x y z)
Completion of rl_theory
(RULES f(i(x),x) → ef(x,f(e,y)) → f(x,y)f(e,i(x)) → i(x)f(e,f(i(x),y)) → f(i(x),y)i(f(x,y)) → f(i(y),i(x))f(x,f(y,f(i(y),z))) → f(x,z)f(x,f(y,i(y))) → x,i(i(x)) → f(e,x)i(e) → ef(i(x),f(x,y)) → f(e,y)f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
3.88
Statisticsiterations: 8 equalities (active): 91 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 3.428 time/normalization: 0.2 time/overlaps: 0.126 time/orientation constraints: 0.508 time/project: 0 time/sat: 0.439 time/update context: 0.077 Convergent TRS(VAR x y z)
Completion of rl_theory
(RULES f(i(x),x) → ef(x,f(e,y)) → f(x,y)f(e,i(x)) → i(x)f(x,f(y,f(i(y),z))) → f(x,z)f(e,f(i(x),y)) → f(i(x),y)i(f(x,y)) → f(i(y),i(x))f(x,f(y,i(y))) → x,i(i(x)) → f(e,x)i(e) → ef(i(x),f(x,y)) → f(e,y)f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
slothrop_ackermann |
0.02
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_ackermann
(RULES a(z,x) → s(x)a(s(x),z) → a(x,s(z))a(s(x),s(y)) → a(x,a(s(x),y))) |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.002 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_ackermann
(RULES a(z,x) → s(x)a(s(x),z) → a(x,s(z))a(s(x),s(y)) → a(x,a(s(x),y))) |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.006 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_ackermann
(RULES a(z,x) → s(x)a(s(x),z) → a(x,s(z))a(s(x),s(y)) → a(x,a(s(x),y))) |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.007 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_ackermann
(RULES a(z,x) → s(x)a(s(x),z) → a(x,s(z))a(s(x),s(y)) → a(x,a(s(x),y))) |
0.03
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.024 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.023 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_ackermann
(RULES a(z,x) → s(x)a(s(x),z) → a(x,s(z))a(s(x),s(y)) → a(x,a(s(x),y))) |
0.01
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_ackermann
(RULES a(z,x) → s(x)a(s(x),z) → a(x,s(z))a(s(x),s(y)) → a(x,a(s(x),y))) |
slothrop_cge | ∞ |
3.57
Statisticsiterations: 8 equalities (active): 133 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.017 time/maxk: 2.807 time/normalization: 0.264 time/overlaps: 0.247 time/orientation constraints: 1.039 time/project: 0 time/sat: 0.61 time/update context: 0.139 Convergent TRS(VAR x y z)
Completion of slothrop_cge
(RULES trans(f(x),g(y)) → trans(g(y),f(x))trans(g(x),g(y)) → g(trans(x,y))trans(f(x),f(y)) → f(trans(x,y))trans(symm(x),x) → refltrans(g(x),trans(g(y),z)) → trans(g(trans(x,y)),z)trans(f(x),trans(g(y),z)) → trans(g(y),trans(f(x),z))trans(f(x),trans(f(y),z)) → trans(f(trans(x,y)),z)trans(x,symm(x)) → reflsymm(f(x)) → f(symm(x))symm(g(x)) → g(symm(x))symm(trans(x,y)) → trans(symm(y),symm(x))trans(x,trans(symm(x),y)) → y,symm(refl) → reflsymm(symm(x)) → x,g(refl) → reflf(refl) → refltrans(x,refl) → x,trans(symm(x),trans(x,y)) → y,trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,) |
157.67
Statisticsiterations: 22 equalities (active): 384 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 16.953 time/maxk: 40.388 time/normalization: 39.301 time/overlaps: 8.538 time/orientation constraints: 17.327 time/project: 0 time/sat: 2.643 time/update context: 0.445 Convergent TRS(VAR x y z)
Completion of slothrop_cge
(RULES trans(f(x),g(y)) → trans(g(y),f(x))trans(g(x),g(y)) → g(trans(x,y))trans(f(x),f(y)) → f(trans(x,y))trans(symm(x),x) → refltrans(f(x),trans(f(y),z)) → trans(f(trans(x,y)),z)trans(f(x),trans(g(y),z)) → trans(g(y),trans(f(x),z))trans(g(x),trans(g(y),z)) → trans(g(trans(x,y)),z)trans(x,symm(x)) → reflsymm(g(x)) → g(symm(x))symm(f(x)) → f(symm(x))symm(trans(x,y)) → trans(symm(y),symm(x))g(refl) → reflf(refl) → reflsymm(refl) → reflsymm(symm(x)) → x,trans(x,refl) → x,trans(x,trans(symm(x),y)) → y,trans(symm(x),trans(x,y)) → y,trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,) |
568.41
Statisticsiterations: 39 equalities (active): 234 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 68.509 time/maxk: 151.222 time/normalization: 142.979 time/overlaps: 10.444 time/orientation constraints: 16.052 time/project: 0 time/sat: 2.013 time/update context: 34.128 Convergent TRS(VAR x y z)
Completion of slothrop_cge
(RULES trans(g(x),g(y)) → g(trans(x,y))trans(f(x),f(y)) → f(trans(x,y))trans(symm(x),x) → refltrans(f(x),trans(f(y),z)) → trans(f(trans(x,y)),z)trans(g(x),trans(g(y),z)) → trans(g(trans(x,y)),z)trans(x,symm(x)) → reflsymm(g(x)) → g(symm(x))symm(f(x)) → f(symm(x))symm(trans(x,y)) → trans(symm(y),symm(x))g(refl) → reflf(refl) → reflsymm(refl) → reflsymm(symm(x)) → x,trans(x,refl) → x,trans(x,trans(symm(x),y)) → y,trans(symm(x),trans(x,y)) → y,trans(g(x),trans(f(y),z)) → trans(f(y),trans(g(x),z))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(g(x),f(y)) → trans(f(y),g(x))) |
15.54
Statisticsiterations: 7 equalities (active): 108 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.032 time/maxk: 14.684 time/normalization: 0.286 time/overlaps: 0.342 time/orientation constraints: 0.94 time/project: 0 time/sat: 9.209 time/update context: 0.025 Convergent TRS(VAR x y z)
Completion of slothrop_cge
(RULES trans(g(x),g(y)) → g(trans(x,y))trans(f(x),f(y)) → f(trans(x,y))trans(symm(x),x) → refltrans(f(x),trans(f(y),z)) → trans(f(trans(x,y)),z)trans(g(x),trans(g(y),z)) → trans(g(trans(x,y)),z)trans(x,symm(x)) → reflsymm(g(x)) → g(symm(x))symm(f(x)) → f(symm(x))symm(trans(x,y)) → trans(symm(y),symm(x))g(refl) → reflf(refl) → reflsymm(refl) → reflsymm(symm(x)) → x,trans(x,refl) → x,trans(x,trans(symm(x),y)) → y,trans(symm(x),trans(x,y)) → y,trans(g(x),trans(f(y),z)) → trans(f(y),trans(g(x),z))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(g(x),f(y)) → trans(f(y),g(x))) |
17.05
Statisticsiterations: 8 equalities (active): 119 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.026 time/maxk: 16.235 time/normalization: 0.303 time/overlaps: 0.215 time/orientation constraints: 0.953 time/project: 0 time/sat: 9.412 time/update context: 0.172 Convergent TRS(VAR x y z)
Completion of slothrop_cge
(RULES trans(f(x),g(y)) → trans(g(y),f(x))trans(g(x),g(y)) → g(trans(x,y))trans(f(x),f(y)) → f(trans(x,y))trans(symm(x),x) → refltrans(g(x),trans(g(y),z)) → trans(g(trans(x,y)),z)trans(f(x),trans(g(y),z)) → trans(g(y),trans(f(x),z))trans(f(x),trans(f(y),z)) → trans(f(trans(x,y)),z)trans(x,symm(x)) → reflsymm(f(x)) → f(symm(x))symm(g(x)) → g(symm(x))symm(trans(x,y)) → trans(symm(y),symm(x))f(refl) → reflg(refl) → reflsymm(refl) → reflsymm(symm(x)) → x,trans(x,refl) → x,trans(x,trans(symm(x),y)) → y,trans(symm(x),trans(x,y)) → y,trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,) |
slothrop_cge3 | ∞ |
4.17
Statisticsiterations: 7 equalities (active): 108 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.027 time/maxk: 3.133 time/normalization: 0.353 time/overlaps: 0.404 time/orientation constraints: 1.014 time/project: 0 time/sat: 1.214 time/update context: 0.09 Convergent TRS(VAR x y z)
Completion of slothrop_cge3
(RULES trans(f(x),g(y)) → trans(g(y),f(x))trans(h(x),h(y)) → h(trans(x,y))trans(g(x),g(y)) → g(trans(x,y))trans(f(x),f(y)) → f(trans(x,y))trans(symm(x),x) → refltrans(f(x),trans(g(y),z)) → trans(g(y),trans(f(x),z))trans(f(x),trans(f(y),z)) → trans(f(trans(x,y)),z)trans(g(x),trans(g(y),z)) → trans(g(trans(x,y)),z)trans(h(x),trans(h(y),z)) → trans(h(trans(x,y)),z)trans(x,symm(x)) → reflsymm(h(x)) → h(symm(x))symm(g(x)) → g(symm(x))symm(f(x)) → f(symm(x))trans(x,trans(symm(x),y)) → y,symm(trans(x,y)) → trans(symm(y),symm(x))g(refl) → reflf(refl) → reflsymm(refl) → reflh(refl) → reflsymm(symm(x)) → x,trans(x,refl) → x,trans(symm(x),trans(x,y)) → y,trans(h(x),trans(g(y),z)) → trans(g(y),trans(h(x),z))trans(h(x),trans(f(y),z)) → trans(f(y),trans(h(x),z))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(h(x),g(y)) → trans(g(y),h(x))trans(h(x),f(y)) → trans(f(y),h(x))) |
180.81
Statisticsiterations: 25 equalities (active): 359 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 23.72 time/maxk: 33.552 time/normalization: 47.366 time/overlaps: 7.706 time/orientation constraints: 14.521 time/project: 0 time/sat: 2.07 time/update context: 0.376 Convergent TRS(VAR x y z)
Completion of slothrop_cge3
(RULES trans(f(x),g(y)) → trans(g(y),f(x))trans(h(x),h(y)) → h(trans(x,y))trans(g(x),g(y)) → g(trans(x,y))trans(f(x),f(y)) → f(trans(x,y))trans(symm(x),x) → refltrans(f(x),trans(g(y),z)) → trans(g(y),trans(f(x),z))trans(f(x),trans(f(y),z)) → trans(f(trans(x,y)),z)trans(g(x),trans(g(y),z)) → trans(g(trans(x,y)),z)trans(h(x),trans(h(y),z)) → trans(h(trans(x,y)),z)trans(x,symm(x)) → reflsymm(h(x)) → h(symm(x))symm(g(x)) → g(symm(x))symm(f(x)) → f(symm(x))symm(trans(x,y)) → trans(symm(y),symm(x))h(refl) → reflg(refl) → reflf(refl) → reflsymm(refl) → reflsymm(symm(x)) → x,trans(x,refl) → x,trans(x,trans(symm(x),y)) → y,trans(symm(x),trans(x,y)) → y,trans(h(x),trans(f(y),z)) → trans(f(y),trans(h(x),z))trans(h(x),trans(g(y),z)) → trans(g(y),trans(h(x),z))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(h(x),g(y)) → trans(g(y),h(x))trans(h(x),f(y)) → trans(f(y),h(x))) |
335.23
Statisticsiterations: 20 equalities (active): 314 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 46.075 time/maxk: 77.038 time/normalization: 87.75 time/overlaps: 8.147 time/orientation constraints: 10.07 time/project: 0 time/sat: 1.625 time/update context: 24.236 Convergent TRS(VAR x y z)
Completion of slothrop_cge3
(RULES trans(g(x),h(y)) → trans(h(y),g(x))trans(h(x),h(y)) → h(trans(x,y))trans(g(x),g(y)) → g(trans(x,y))trans(f(x),f(y)) → f(trans(x,y))trans(symm(x),x) → refltrans(g(x),trans(g(y),z)) → trans(g(trans(x,y)),z)trans(g(x),trans(h(y),z)) → trans(h(y),trans(g(x),z))trans(f(x),trans(f(y),z)) → trans(f(trans(x,y)),z)trans(h(x),trans(h(y),z)) → trans(h(trans(x,y)),z)trans(x,symm(x)) → reflsymm(h(x)) → h(symm(x))symm(g(x)) → g(symm(x))symm(f(x)) → f(symm(x))symm(trans(x,y)) → trans(symm(y),symm(x))h(refl) → reflg(refl) → reflf(refl) → reflsymm(refl) → reflsymm(symm(x)) → x,trans(x,refl) → x,trans(x,trans(symm(x),y)) → y,trans(symm(x),trans(x,y)) → y,trans(h(x),trans(f(y),z)) → trans(f(y),trans(h(x),z))trans(g(x),trans(f(y),z)) → trans(f(y),trans(g(x),z))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(g(x),f(y)) → trans(f(y),g(x))trans(h(x),f(y)) → trans(f(y),h(x))) |
19.08
Statisticsiterations: 7 equalities (active): 107 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.043 time/maxk: 18.044 time/normalization: 0.324 time/overlaps: 0.352 time/orientation constraints: 0.711 time/project: 0 time/sat: 12.678 time/update context: 0.028 Convergent TRS(VAR x y z)
Completion of slothrop_cge3
(RULES trans(f(x),h(y)) → trans(h(y),f(x))trans(f(x),g(y)) → trans(g(y),f(x))trans(h(x),h(y)) → h(trans(x,y))trans(g(x),g(y)) → g(trans(x,y))trans(f(x),f(y)) → f(trans(x,y))trans(symm(x),x) → refltrans(f(x),trans(g(y),z)) → trans(g(y),trans(f(x),z))trans(f(x),trans(h(y),z)) → trans(h(y),trans(f(x),z))trans(f(x),trans(f(y),z)) → trans(f(trans(x,y)),z)trans(g(x),trans(g(y),z)) → trans(g(trans(x,y)),z)trans(h(x),trans(h(y),z)) → trans(h(trans(x,y)),z)trans(x,symm(x)) → reflsymm(h(x)) → h(symm(x))symm(g(x)) → g(symm(x))symm(f(x)) → f(symm(x))symm(trans(x,y)) → trans(symm(y),symm(x))h(refl) → reflg(refl) → reflf(refl) → reflsymm(refl) → reflsymm(symm(x)) → x,trans(x,refl) → x,trans(x,trans(symm(x),y)) → y,trans(symm(x),trans(x,y)) → y,trans(h(x),trans(g(y),z)) → trans(g(y),trans(h(x),z))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(h(x),g(y)) → trans(g(y),h(x))) |
9.24
Statisticsiterations: 7 equalities (active): 103 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.03 time/maxk: 8.505 time/normalization: 0.256 time/overlaps: 0.237 time/orientation constraints: 0.573 time/project: 0 time/sat: 4.865 time/update context: 0.083 Convergent TRS(VAR x y z)
Completion of slothrop_cge3
(RULES trans(f(x),h(y)) → trans(h(y),f(x))trans(g(x),h(y)) → trans(h(y),g(x))trans(f(x),g(y)) → trans(g(y),f(x))trans(h(x),h(y)) → h(trans(x,y))trans(g(x),g(y)) → g(trans(x,y))trans(f(x),f(y)) → f(trans(x,y))trans(symm(x),x) → refltrans(g(x),trans(g(y),z)) → trans(g(trans(x,y)),z)trans(f(x),trans(g(y),z)) → trans(g(y),trans(f(x),z))trans(g(x),trans(h(y),z)) → trans(h(y),trans(g(x),z))trans(f(x),trans(h(y),z)) → trans(h(y),trans(f(x),z))trans(f(x),trans(f(y),z)) → trans(f(trans(x,y)),z)trans(h(x),trans(h(y),z)) → trans(h(trans(x,y)),z)trans(x,symm(x)) → reflsymm(h(x)) → h(symm(x))symm(g(x)) → g(symm(x))symm(f(x)) → f(symm(x))symm(trans(x,y)) → trans(symm(y),symm(x))h(refl) → reflg(refl) → reflf(refl) → reflsymm(refl) → reflsymm(symm(x)) → x,trans(x,refl) → x,trans(x,trans(symm(x),y)) → y,trans(symm(x),trans(x,y)) → y,trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,) |
slothrop_endo | ∞ |
1.95
Statisticsiterations: 7 equalities (active): 94 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.01 time/maxk: 1.549 time/normalization: 0.143 time/overlaps: 0.139 time/orientation constraints: 0.663 time/project: 0 time/sat: 0.216 time/update context: 0.098 Convergent TRS(VAR x y z)
Completion of slothrop_endo
(RULES f(x,i(x)) → ef(i(x),x) → ei(f(x,y)) → f(i(y),i(x))h(i(x)) → i(h(x))i(e) → ei(i(x)) → x,f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,h(e) → ef(e,x) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,h(f(x,y)) → f(h(x),h(y))) |
55.27
Statisticsiterations: 17 equalities (active): 289 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 2.555 time/maxk: 19.191 time/normalization: 14.037 time/overlaps: 4.781 time/orientation constraints: 10.266 time/project: 0 time/sat: 1.103 time/update context: 0.187 Convergent TRS(VAR x y z)
Completion of slothrop_endo
(RULES f(x,i(x)) → ef(i(x),x) → ei(f(x,y)) → f(i(y),i(x))i(e) → ei(i(x)) → x,h(i(x)) → i(h(x))f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,h(e) → ef(e,x) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,h(f(x,y)) → f(h(x),h(y))) |
1.27
Statisticsiterations: 7 equalities (active): 99 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.008 time/maxk: 0.929 time/normalization: 0.137 time/overlaps: 0.089 time/orientation constraints: 0.425 time/project: 0 time/sat: 0.072 time/update context: 0.05 Convergent TRS(VAR x y z)
Completion of slothrop_endo
(RULES f(x,i(x)) → ef(i(x),x) → ei(f(x,y)) → f(i(y),i(x))i(e) → ei(i(x)) → x,h(i(x)) → i(h(x))f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,h(e) → ef(e,x) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,h(f(x,y)) → f(h(x),h(y))) |
6.06
Statisticsiterations: 7 equalities (active): 102 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.015 time/maxk: 5.545 time/normalization: 0.192 time/overlaps: 0.182 time/orientation constraints: 0.612 time/project: 0 time/sat: 1.169 time/update context: 0.021 Convergent TRS(VAR x y z)
Completion of slothrop_endo
(RULES f(x,i(x)) → ef(x,f(i(x),y)) → y,f(i(x),x) → ei(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,i(e) → ei(i(x)) → x,h(i(x)) → i(h(x))h(e) → ef(e,x) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,h(f(x,y)) → f(h(x),h(y))) |
5.35
Statisticsiterations: 8 equalities (active): 118 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.012 time/maxk: 4.884 time/normalization: 0.211 time/overlaps: 0.11 time/orientation constraints: 0.488 time/project: 0 time/sat: 0.712 time/update context: 0.094 Convergent TRS(VAR x y z)
Completion of slothrop_endo
(RULES f(x,i(x)) → ef(x,f(i(x),y)) → y,f(i(x),x) → ei(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,i(e) → ei(i(x)) → x,h(i(x)) → i(h(x))h(e) → ef(e,x) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,h(f(x,y)) → f(h(x),h(y))) |
slothrop_equiv_proofs |
3.89
Statisticsiterations: 4 equalities (active): 78 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.012 time/maxk: 1.056 time/normalization: 0.989 time/overlaps: 1.155 time/orientation constraints: 0.805 time/project: 0 time/sat: 0.143 time/update context: 0.017 Convergent TRS(VAR x1 x2 x3)
Completion of slothrop_equiv_proofs
(RULES trans(ortrue2,x1) → ortrue2trans(ortrue1,x1) → ortrue1trans(congror1(x1),orfalse2) → trans(orfalse2,x1)trans(congror2(x1),orfalse1) → trans(orfalse1,x1)trans(congror2(x1),ortrue1) → ortrue1trans(congror1(x1),ortrue2) → ortrue2trans(congror1(x1),trans(orfalse2,x2)) → trans(orfalse2,trans(x1,x2))trans(congror2(x1),trans(orfalse1,x2)) → trans(orfalse1,trans(x1,x2))trans(congror1(x1),congror2(x2)) → trans(congror2(x2),congror1(x1))trans(congror2(x1),congror2(x2)) → congror2(trans(x1,x2))trans(congror1(x1),congror1(x2)) → congror1(trans(x1,x2))trans(congror1(x1),trans(congror2(x2),x3)) → trans(congror2(x2),trans(congror1(x1),x3))trans(congror2(x1),trans(congror2(x2),x3)) → trans(congror2(trans(x1,x2)),x3)trans(congror1(x1),trans(congror1(x2),x3)) → trans(congror1(trans(x1,x2)),x3)trans(congror2(x1),trans(congror1(x2),orfalse1)) → trans(congror1(x2),trans(orfalse1,x1))trans(congror2(x1),trans(congror1(x2),ortrue1)) → trans(congror1(x2),ortrue1)trans(congror2(x1),trans(congror1(x2),trans(orfalse1,x3))) → trans(congror1(x2),trans(orfalse1,trans(x1,x3)))trans(trans(x1,x2),x3) → trans(x1,trans(x2,x3))trans(refl,x1) → x1,trans(x1,refl) → x1,congror1(refl) → reflcongror2(refl) → refl) |
3.76
Statisticsiterations: 6 equalities (active): 108 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.01 time/maxk: 3.215 time/normalization: 0.243 time/overlaps: 0.147 time/orientation constraints: 1.405 time/project: 0 time/sat: 0.787 time/update context: 0.121 Convergent TRS(VAR x1 x2 x3)
Completion of slothrop_equiv_proofs
(RULES trans(ortrue2,x1) → ortrue2trans(ortrue1,x1) → ortrue1trans(congror1(x1),orfalse2) → trans(orfalse2,x1)trans(congror2(x1),orfalse1) → trans(orfalse1,x1)trans(congror2(x1),ortrue1) → ortrue1trans(congror1(x1),ortrue2) → ortrue2trans(congror2(x1),trans(orfalse1,x2)) → trans(orfalse1,trans(x1,x2))trans(congror1(x1),trans(orfalse2,x2)) → trans(orfalse2,trans(x1,x2))trans(congror1(x1),congror2(x2)) → trans(congror2(x2),congror1(x1))trans(congror2(x1),congror2(x2)) → congror2(trans(x1,x2))trans(congror1(x1),congror1(x2)) → congror1(trans(x1,x2))trans(congror1(x1),trans(congror2(x2),x3)) → trans(congror2(x2),trans(congror1(x1),x3))trans(congror2(x1),trans(congror2(x2),x3)) → trans(congror2(trans(x1,x2)),x3)trans(congror1(x1),trans(congror1(x2),x3)) → trans(congror1(trans(x1,x2)),x3)trans(congror2(x1),trans(congror1(x2),trans(orfalse1,x3))) → trans(congror1(x2),trans(orfalse1,trans(x1,x3)))trans(congror2(x1),trans(congror1(x2),orfalse1)) → trans(congror1(x2),trans(orfalse1,x1))trans(congror2(x1),trans(congror1(x2),ortrue1)) → trans(congror1(x2),ortrue1)trans(trans(x1,x2),x3) → trans(x1,trans(x2,x3))trans(refl,x1) → x1,trans(x1,refl) → x1,congror1(refl) → reflcongror2(refl) → refl) |
2.13
Statisticsiterations: 6 equalities (active): 102 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 1.734 time/normalization: 0.097 time/overlaps: 0.125 time/orientation constraints: 1.25 time/project: 0 time/sat: 0.121 time/update context: 0.013 Convergent TRS(VAR x1 x2 x3)
Completion of slothrop_equiv_proofs
(RULES trans(ortrue2,x1) → ortrue2trans(ortrue1,x1) → ortrue1trans(congror1(x1),orfalse2) → trans(orfalse2,x1)trans(congror2(x1),orfalse1) → trans(orfalse1,x1)trans(congror2(x1),ortrue1) → ortrue1trans(congror1(x1),ortrue2) → ortrue2trans(x1,trans(x2,x3)) → trans(trans(x1,x2),x3)trans(trans(x1,congror2(x2)),orfalse1) → trans(trans(x1,orfalse1),x2)trans(trans(x1,congror1(x2)),orfalse2) → trans(trans(x1,orfalse2),x2)trans(trans(congror2(x1),congror1(x2)),ortrue1) → trans(congror1(x2),ortrue1)trans(congror1(x1),congror2(x2)) → trans(congror2(x2),congror1(x1))trans(congror2(x1),congror2(x2)) → congror2(trans(x1,x2))trans(congror1(x1),congror1(x2)) → congror1(trans(x1,x2))trans(trans(x1,congror1(x2)),congror2(x3)) → trans(trans(x1,congror2(x3)),congror1(x2))trans(trans(trans(x1,congror2(x2)),congror1(x3)),orfalse1) → trans(trans(trans(x1,congror1(x3)),orfalse1),x2)trans(trans(x1,congror2(x2)),congror2(x3)) → trans(x1,congror2(trans(x2,x3)))trans(trans(x1,congror1(x2)),congror1(x3)) → trans(x1,congror1(trans(x2,x3)))trans(trans(congror2(x1),congror1(x2)),orfalse1) → trans(trans(congror1(x2),orfalse1),x1)trans(trans(trans(x1,congror2(x2)),congror1(x3)),ortrue1) → trans(trans(x1,congror1(x3)),ortrue1)trans(trans(x1,ortrue2),x2) → trans(x1,ortrue2)trans(trans(x1,ortrue1),x2) → trans(x1,ortrue1)trans(trans(x1,congror2(x2)),ortrue1) → trans(x1,ortrue1)trans(trans(x1,congror1(x2)),ortrue2) → trans(x1,ortrue2)trans(refl,x1) → x1,trans(x1,refl) → x1,congror1(refl) → reflcongror2(refl) → refl) |
2.21
Statisticsiterations: 5 equalities (active): 114 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 1.812 time/normalization: 0.117 time/overlaps: 0.119 time/orientation constraints: 0.983 time/project: 0 time/sat: 0.1 time/update context: 0.08 Convergent TRS(VAR x1 x2 x3)
Completion of slothrop_equiv_proofs
(RULES trans(ortrue2,x1) → ortrue2trans(ortrue1,x1) → ortrue1trans(congror1(x1),orfalse2) → trans(orfalse2,x1)trans(congror2(x1),orfalse1) → trans(orfalse1,x1)trans(congror2(x1),ortrue1) → ortrue1trans(congror1(x1),ortrue2) → ortrue2trans(congror2(x1),trans(orfalse1,x2)) → trans(orfalse1,trans(x1,x2))trans(congror1(x1),trans(orfalse2,x2)) → trans(orfalse2,trans(x1,x2))trans(congror1(x1),congror2(x2)) → trans(congror2(x2),congror1(x1))trans(congror1(x1),congror1(x2)) → congror1(trans(x1,x2))trans(congror2(x1),congror2(x2)) → congror2(trans(x1,x2))trans(congror1(x1),trans(congror2(x2),x3)) → trans(congror2(x2),trans(congror1(x1),x3))trans(congror1(x1),trans(congror1(x2),x3)) → trans(congror1(trans(x1,x2)),x3)trans(congror2(x1),trans(congror2(x2),x3)) → trans(congror2(trans(x1,x2)),x3)trans(congror2(x1),trans(congror1(x2),orfalse1)) → trans(congror1(x2),trans(orfalse1,x1))trans(congror2(x1),trans(congror1(x2),trans(orfalse1,x3))) → trans(congror1(x2),trans(orfalse1,trans(x1,x3)))trans(congror2(x1),trans(congror1(x2),ortrue1)) → trans(congror1(x2),ortrue1)trans(trans(x1,x2),x3) → trans(x1,trans(x2,x3))trans(refl,x1) → x1,trans(x1,refl) → x1,congror1(refl) → reflcongror2(refl) → refl) |
3.40
Statisticsiterations: 6 equalities (active): 95 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 3.02 time/normalization: 0.121 time/overlaps: 0.137 time/orientation constraints: 1.435 time/project: 0 time/sat: 0.459 time/update context: 0.018 Convergent TRS(VAR x1 x2 x3)
Completion of slothrop_equiv_proofs
(RULES trans(ortrue2,x1) → ortrue2trans(ortrue1,x1) → ortrue1trans(congror1(x1),orfalse2) → trans(orfalse2,x1)trans(congror2(x1),orfalse1) → trans(orfalse1,x1)trans(congror2(x1),ortrue1) → ortrue1trans(congror1(x1),ortrue2) → ortrue2trans(congror1(x1),trans(orfalse2,x2)) → trans(orfalse2,trans(x1,x2))trans(congror2(x1),trans(orfalse1,x2)) → trans(orfalse1,trans(x1,x2))trans(congror1(x1),congror2(x2)) → trans(congror2(x2),congror1(x1))trans(congror2(x1),congror2(x2)) → congror2(trans(x1,x2))trans(congror1(x1),congror1(x2)) → congror1(trans(x1,x2))trans(congror1(x1),trans(congror2(x2),x3)) → trans(congror2(x2),trans(congror1(x1),x3))trans(congror1(x1),trans(congror1(x2),x3)) → trans(congror1(trans(x1,x2)),x3)trans(congror2(x1),trans(congror2(x2),x3)) → trans(congror2(trans(x1,x2)),x3)trans(congror2(x1),trans(congror1(x2),orfalse1)) → trans(congror1(x2),trans(orfalse1,x1))trans(congror2(x1),trans(congror1(x2),ortrue1)) → trans(congror1(x2),ortrue1)trans(congror2(x1),trans(congror1(x2),trans(orfalse1,x3))) → trans(congror1(x2),trans(orfalse1,trans(x1,x3)))trans(trans(x1,x2),x3) → trans(x1,trans(x2,x3))trans(refl,x1) → x1,trans(x1,refl) → x1,congror1(refl) → reflcongror2(refl) → refl) |
3.14
Statisticsiterations: 5 equalities (active): 93 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 2.776 time/normalization: 0.123 time/overlaps: 0.125 time/orientation constraints: 1.004 time/project: 0 time/sat: 0.41 time/update context: 0.049 Convergent TRS(VAR x1 x2 x3)
Completion of slothrop_equiv_proofs
(RULES trans(ortrue2,x1) → ortrue2trans(ortrue1,x1) → ortrue1trans(congror1(x1),orfalse2) → trans(orfalse2,x1)trans(congror2(x1),orfalse1) → trans(orfalse1,x1)trans(congror2(x1),ortrue1) → ortrue1trans(congror1(x1),ortrue2) → ortrue2trans(congror2(x1),trans(orfalse1,x2)) → trans(orfalse1,trans(x1,x2))trans(congror1(x1),trans(orfalse2,x2)) → trans(orfalse2,trans(x1,x2))trans(congror1(x1),congror2(x2)) → trans(congror2(x2),congror1(x1))trans(congror1(x1),congror1(x2)) → congror1(trans(x1,x2))trans(congror2(x1),congror2(x2)) → congror2(trans(x1,x2))trans(congror1(x1),trans(congror2(x2),x3)) → trans(congror2(x2),trans(congror1(x1),x3))trans(congror1(x1),trans(congror1(x2),x3)) → trans(congror1(trans(x1,x2)),x3)trans(congror2(x1),trans(congror2(x2),x3)) → trans(congror2(trans(x1,x2)),x3)trans(congror2(x1),trans(congror1(x2),orfalse1)) → trans(congror1(x2),trans(orfalse1,x1))trans(congror2(x1),trans(congror1(x2),ortrue1)) → trans(congror1(x2),ortrue1)trans(congror2(x1),trans(congror1(x2),trans(orfalse1,x3))) → trans(congror1(x2),trans(orfalse1,trans(x1,x3)))trans(trans(x1,x2),x3) → trans(x1,trans(x2,x3))trans(refl,x1) → x1,trans(x1,refl) → x1,congror1(refl) → reflcongror2(refl) → refl) |
slothrop_equiv_proofs_or |
3.84
Statisticsiterations: 4 equalities (active): 78 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.014 time/maxk: 0.992 time/normalization: 1.005 time/overlaps: 1.153 time/orientation constraints: 0.757 time/project: 0 time/sat: 0.143 time/update context: 0.006 Convergent TRS(VAR x y z)
Completion of slothrop_equiv_proofs_or
(RULES trans(ortrue2,x) → ortrue2trans(ortrue1,x) → ortrue1trans(congror1(x),orfalse2) → trans(orfalse2,x)trans(congror2(x),orfalse1) → trans(orfalse1,x)trans(congror2(x),ortrue1) → ortrue1trans(congror1(x),ortrue2) → ortrue2trans(congror1(x),trans(orfalse2,y)) → trans(orfalse2,trans(x,y))trans(congror2(x),trans(orfalse1,y)) → trans(orfalse1,trans(x,y))trans(congror1(x),congror2(y)) → trans(congror2(y),congror1(x))trans(congror2(x),congror2(y)) → congror2(trans(x,y))trans(congror1(x),congror1(y)) → congror1(trans(x,y))trans(congror1(x),trans(congror2(y),z)) → trans(congror2(y),trans(congror1(x),z))trans(congror2(x),trans(congror2(y),z)) → trans(congror2(trans(x,y)),z)trans(congror1(x),trans(congror1(y),z)) → trans(congror1(trans(x,y)),z)trans(congror2(x),trans(congror1(y),orfalse1)) → trans(congror1(y),trans(orfalse1,x))trans(congror2(x),trans(congror1(y),ortrue1)) → trans(congror1(y),ortrue1)trans(congror2(x),trans(congror1(y),trans(orfalse1,z))) → trans(congror1(y),trans(orfalse1,trans(x,z)))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(x,refl) → x,congror1(refl) → reflcongror2(refl) → refl) |
3.34
Statisticsiterations: 6 equalities (active): 108 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 2.863 time/normalization: 0.192 time/overlaps: 0.134 time/orientation constraints: 1.167 time/project: 0 time/sat: 0.703 time/update context: 0.122 Convergent TRS(VAR x y z)
Completion of slothrop_equiv_proofs_or
(RULES trans(ortrue2,x) → ortrue2trans(ortrue1,x) → ortrue1trans(congror1(x),orfalse2) → trans(orfalse2,x)trans(congror2(x),orfalse1) → trans(orfalse1,x)trans(congror2(x),ortrue1) → ortrue1trans(congror1(x),ortrue2) → ortrue2trans(congror2(x),trans(orfalse1,y)) → trans(orfalse1,trans(x,y))trans(congror1(x),trans(orfalse2,y)) → trans(orfalse2,trans(x,y))trans(congror1(x),congror2(y)) → trans(congror2(y),congror1(x))trans(congror2(x),congror2(y)) → congror2(trans(x,y))trans(congror1(x),congror1(y)) → congror1(trans(x,y))trans(congror1(x),trans(congror2(y),z)) → trans(congror2(y),trans(congror1(x),z))trans(congror2(x),trans(congror2(y),z)) → trans(congror2(trans(x,y)),z)trans(congror1(x),trans(congror1(y),z)) → trans(congror1(trans(x,y)),z)trans(congror2(x),trans(congror1(y),trans(orfalse1,z))) → trans(congror1(y),trans(orfalse1,trans(x,z)))trans(congror2(x),trans(congror1(y),orfalse1)) → trans(congror1(y),trans(orfalse1,x))trans(congror2(x),trans(congror1(y),ortrue1)) → trans(congror1(y),ortrue1)trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(x,refl) → x,congror1(refl) → reflcongror2(refl) → refl) |
2.36
Statisticsiterations: 6 equalities (active): 102 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 1.927 time/normalization: 0.111 time/overlaps: 0.145 time/orientation constraints: 1.389 time/project: 0 time/sat: 0.139 time/update context: 0.014 Convergent TRS(VAR x y z)
Completion of slothrop_equiv_proofs_or
(RULES trans(ortrue2,x) → ortrue2trans(ortrue1,x) → ortrue1trans(congror1(x),orfalse2) → trans(orfalse2,x)trans(congror2(x),orfalse1) → trans(orfalse1,x)trans(congror2(x),ortrue1) → ortrue1trans(congror1(x),ortrue2) → ortrue2trans(x,trans(y,z)) → trans(trans(x,y),z)trans(trans(x,congror2(y)),orfalse1) → trans(trans(x,orfalse1),y)trans(trans(x,congror1(y)),orfalse2) → trans(trans(x,orfalse2),y)trans(trans(congror2(x),congror1(y)),ortrue1) → trans(congror1(y),ortrue1)trans(congror1(x),congror2(y)) → trans(congror2(y),congror1(x))trans(congror2(x),congror2(y)) → congror2(trans(x,y))trans(congror1(x),congror1(y)) → congror1(trans(x,y))trans(trans(x,congror1(y)),congror2(z)) → trans(trans(x,congror2(z)),congror1(y))trans(trans(trans(x,congror2(y)),congror1(z)),orfalse1) → trans(trans(trans(x,congror1(z)),orfalse1),y)trans(trans(x,congror2(y)),congror2(z)) → trans(x,congror2(trans(y,z)))trans(trans(x,congror1(y)),congror1(z)) → trans(x,congror1(trans(y,z)))trans(trans(congror2(x),congror1(y)),orfalse1) → trans(trans(congror1(y),orfalse1),x)trans(trans(trans(x,congror2(y)),congror1(z)),ortrue1) → trans(trans(x,congror1(z)),ortrue1)trans(trans(x,ortrue2),y) → trans(x,ortrue2)trans(trans(x,ortrue1),y) → trans(x,ortrue1)trans(trans(x,congror2(y)),ortrue1) → trans(x,ortrue1)trans(trans(x,congror1(y)),ortrue2) → trans(x,ortrue2)trans(refl,x) → x,trans(x,refl) → x,congror1(refl) → reflcongror2(refl) → refl) |
2.68
Statisticsiterations: 5 equalities (active): 114 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 2.193 time/normalization: 0.146 time/overlaps: 0.149 time/orientation constraints: 1.218 time/project: 0 time/sat: 0.107 time/update context: 0.089 Convergent TRS(VAR x y z)
Completion of slothrop_equiv_proofs_or
(RULES trans(ortrue2,x) → ortrue2trans(ortrue1,x) → ortrue1trans(congror1(x),orfalse2) → trans(orfalse2,x)trans(congror2(x),orfalse1) → trans(orfalse1,x)trans(congror2(x),ortrue1) → ortrue1trans(congror1(x),ortrue2) → ortrue2trans(congror2(x),trans(orfalse1,y)) → trans(orfalse1,trans(x,y))trans(congror1(x),trans(orfalse2,y)) → trans(orfalse2,trans(x,y))trans(congror1(x),congror2(y)) → trans(congror2(y),congror1(x))trans(congror1(x),congror1(y)) → congror1(trans(x,y))trans(congror2(x),congror2(y)) → congror2(trans(x,y))trans(congror1(x),trans(congror2(y),z)) → trans(congror2(y),trans(congror1(x),z))trans(congror1(x),trans(congror1(y),z)) → trans(congror1(trans(x,y)),z)trans(congror2(x),trans(congror2(y),z)) → trans(congror2(trans(x,y)),z)trans(congror2(x),trans(congror1(y),orfalse1)) → trans(congror1(y),trans(orfalse1,x))trans(congror2(x),trans(congror1(y),trans(orfalse1,z))) → trans(congror1(y),trans(orfalse1,trans(x,z)))trans(congror2(x),trans(congror1(y),ortrue1)) → trans(congror1(y),ortrue1)trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(x,refl) → x,congror1(refl) → reflcongror2(refl) → refl) |
3.52
Statisticsiterations: 6 equalities (active): 95 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 3.124 time/normalization: 0.131 time/overlaps: 0.151 time/orientation constraints: 1.447 time/project: 0 time/sat: 0.467 time/update context: 0.019 Convergent TRS(VAR x y z)
Completion of slothrop_equiv_proofs_or
(RULES trans(ortrue2,x) → ortrue2trans(ortrue1,x) → ortrue1trans(congror1(x),orfalse2) → trans(orfalse2,x)trans(congror2(x),orfalse1) → trans(orfalse1,x)trans(congror2(x),ortrue1) → ortrue1trans(congror1(x),ortrue2) → ortrue2trans(congror1(x),trans(orfalse2,y)) → trans(orfalse2,trans(x,y))trans(congror2(x),trans(orfalse1,y)) → trans(orfalse1,trans(x,y))trans(congror1(x),congror2(y)) → trans(congror2(y),congror1(x))trans(congror2(x),congror2(y)) → congror2(trans(x,y))trans(congror1(x),congror1(y)) → congror1(trans(x,y))trans(congror1(x),trans(congror2(y),z)) → trans(congror2(y),trans(congror1(x),z))trans(congror1(x),trans(congror1(y),z)) → trans(congror1(trans(x,y)),z)trans(congror2(x),trans(congror2(y),z)) → trans(congror2(trans(x,y)),z)trans(congror2(x),trans(congror1(y),orfalse1)) → trans(congror1(y),trans(orfalse1,x))trans(congror2(x),trans(congror1(y),ortrue1)) → trans(congror1(y),ortrue1)trans(congror2(x),trans(congror1(y),trans(orfalse1,z))) → trans(congror1(y),trans(orfalse1,trans(x,z)))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(x,refl) → x,congror1(refl) → reflcongror2(refl) → refl) |
3.08
Statisticsiterations: 5 equalities (active): 93 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 2.746 time/normalization: 0.105 time/overlaps: 0.112 time/orientation constraints: 0.947 time/project: 0 time/sat: 0.439 time/update context: 0.056 Convergent TRS(VAR x y z)
Completion of slothrop_equiv_proofs_or
(RULES trans(ortrue2,x) → ortrue2trans(ortrue1,x) → ortrue1trans(congror1(x),orfalse2) → trans(orfalse2,x)trans(congror2(x),orfalse1) → trans(orfalse1,x)trans(congror2(x),ortrue1) → ortrue1trans(congror1(x),ortrue2) → ortrue2trans(congror2(x),trans(orfalse1,y)) → trans(orfalse1,trans(x,y))trans(congror1(x),trans(orfalse2,y)) → trans(orfalse2,trans(x,y))trans(congror1(x),congror2(y)) → trans(congror2(y),congror1(x))trans(congror1(x),congror1(y)) → congror1(trans(x,y))trans(congror2(x),congror2(y)) → congror2(trans(x,y))trans(congror1(x),trans(congror2(y),z)) → trans(congror2(y),trans(congror1(x),z))trans(congror1(x),trans(congror1(y),z)) → trans(congror1(trans(x,y)),z)trans(congror2(x),trans(congror2(y),z)) → trans(congror2(trans(x,y)),z)trans(congror2(x),trans(congror1(y),orfalse1)) → trans(congror1(y),trans(orfalse1,x))trans(congror2(x),trans(congror1(y),ortrue1)) → trans(congror1(y),ortrue1)trans(congror2(x),trans(congror1(y),trans(orfalse1,z))) → trans(congror1(y),trans(orfalse1,trans(x,z)))trans(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(x,refl) → x,congror1(refl) → reflcongror2(refl) → refl) |
slothrop_fgh |
0.02
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0.001 time/overlaps: 0.002 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.001 time/update context: 0.001 Convergent TRS(VAR x y)
Completion of slothrop_fgh
(RULES h(x,y) → ag(x,y) → af(x) → a) |
0.02
Statisticsiterations: 3 equalities (active): 7 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.014 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.009 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_fgh
(RULES g(x,y) → ah(x,y) → af(x) → a) |
0.02
Statisticsiterations: 3 equalities (active): 7 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.011 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.007 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_fgh
(RULES g(x,y) → af(x) → ah(x,y) → a) |
0.01
Statisticsiterations: 3 equalities (active): 7 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.004 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_fgh
(RULES g(x,y) → af(x) → ah(x,y) → a) |
0.01
Statisticsiterations: 3 equalities (active): 7 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_fgh
(RULES g(x,y) → af(x) → ah(x,y) → a) |
0.01
Statisticsiterations: 3 equalities (active): 7 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.01 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.005 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_fgh
(RULES g(x,y) → af(x) → ah(x,y) → a) |
slothrop_groups | ∞ |
0.75
Statisticsiterations: 6 equalities (active): 67 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 0.465 time/normalization: 0.106 time/overlaps: 0.112 time/orientation constraints: 0.15 time/project: 0 time/sat: 0.029 time/update context: 0.039 Convergent TRS(VAR x y z)
Completion of slothrop_groups
(RULES f(x,i(x)) → ef(i(x),x) → ei(f(x,y)) → f(i(y),i(x))i(e) → ei(i(x)) → x,f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,f(e,x) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
2.24
Statisticsiterations: 8 equalities (active): 121 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.01 time/maxk: 1.459 time/normalization: 0.276 time/overlaps: 0.298 time/orientation constraints: 0.752 time/project: 0 time/sat: 0.05 time/update context: 0.024 Convergent TRS(VAR x y z)
Completion of slothrop_groups
(RULES f(x,i(x)) → ef(i(x),x) → ei(f(x,y)) → f(i(y),i(x))i(e) → ei(i(x)) → x,f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,f(e,x) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
0.75
Statisticsiterations: 7 equalities (active): 78 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 0.464 time/normalization: 0.126 time/overlaps: 0.081 time/orientation constraints: 0.118 time/project: 0 time/sat: 0.017 time/update context: 0.037 Convergent TRS(VAR x y z)
Completion of slothrop_groups
(RULES f(x,i(x)) → ef(i(x),x) → ei(f(x,y)) → f(i(y),i(x))i(e) → ei(i(x)) → x,f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,f(e,x) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
1.21
Statisticsiterations: 6 equalities (active): 67 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 1.066 time/normalization: 0.056 time/overlaps: 0.047 time/orientation constraints: 0.103 time/project: 0 time/sat: 0.117 time/update context: 0.006 Convergent TRS(VAR x y z)
Completion of slothrop_groups
(RULES f(x,i(x)) → ef(x,f(i(x),y)) → y,f(i(x),x) → ei(f(x,y)) → f(i(y),i(x))i(e) → ei(i(x)) → x,f(i(x),f(x,y)) → y,f(e,x) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
0.82
Statisticsiterations: 6 equalities (active): 57 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 0.654 time/normalization: 0.069 time/overlaps: 0.056 time/orientation constraints: 0.119 time/project: 0 time/sat: 0.038 time/update context: 0.016 Convergent TRS(VAR x y z)
Completion of slothrop_groups
(RULES f(x,i(x)) → ef(i(x),x) → ef(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,i(f(x,y)) → f(i(y),i(x))i(e) → ei(i(x)) → x,f(e,x) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
slothrop_groups_conj | ∞ |
0.11
Statisticsiterations: 3 equalities (active): 39 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.079 time/normalization: 0.009 time/overlaps: 0.011 time/orientation constraints: 0.046 time/project: 0 time/sat: 0.008 time/update context: 0.002 Convergent TRS(VAR x y z)
Completion of slothrop_groups_conj
(RULES f(x,i(x)) → ef(i(x),x) → ei(i(x)) → x,f(i(x),f(x,y)) → y,i(e) → ef(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(e,x) → x,i(f(x,y)) → f(i(y),i(x))) |
1.49
Statisticsiterations: 6 equalities (active): 90 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.854 time/normalization: 0.282 time/overlaps: 0.17 time/orientation constraints: 0.571 time/project: 0 time/sat: 0.033 time/update context: 0.013 Convergent TRS(VAR x y z)
Completion of slothrop_groups_conj
(RULES f(x,i(x)) → ef(i(x),x) → ei(i(x)) → x,f(i(x),f(x,y)) → y,i(e) → ef(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(e,x) → x,i(f(x,y)) → f(i(y),i(x))) |
0.59
Statisticsiterations: 5 equalities (active): 75 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.39 time/normalization: 0.077 time/overlaps: 0.077 time/orientation constraints: 0.226 time/project: 0 time/sat: 0.019 time/update context: 0.012 Convergent TRS(VAR x y z)
Completion of slothrop_groups_conj
(RULES f(x,i(x)) → ef(i(x),x) → ei(i(x)) → x,f(i(x),f(x,y)) → y,i(e) → ef(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(e,x) → x,i(f(x,y)) → f(i(y),i(x))) |
0.55
Statisticsiterations: 4 equalities (active): 59 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.46 time/normalization: 0.024 time/overlaps: 0.034 time/orientation constraints: 0.16 time/project: 0 time/sat: 0.068 time/update context: 0.003 Convergent TRS(VAR x y z)
Completion of slothrop_groups_conj
(RULES f(x,i(x)) → ef(i(x),x) → ei(i(x)) → x,f(i(x),f(x,y)) → y,i(e) → ef(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(e,x) → x,i(f(x,y)) → f(i(y),i(x))) |
0.56
Statisticsiterations: 4 equalities (active): 59 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.459 time/normalization: 0.043 time/overlaps: 0.032 time/orientation constraints: 0.124 time/project: 0 time/sat: 0.059 time/update context: 0.024 Convergent TRS(VAR x y z)
Completion of slothrop_groups_conj
(RULES f(x,i(x)) → ef(i(x),x) → ei(i(x)) → x,f(i(x),f(x,y)) → y,i(e) → ef(x,f(i(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,f(e,x) → x,i(f(x,y)) → f(i(y),i(x))) |
slothrop_hard |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.006 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_hard
(RULES plus(x,s(y)) → s(plus(x,y))plus(x,z) → x,) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_hard
(RULES plus(x,s(y)) → s(plus(x,y))plus(x,z) → x,) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_hard
(RULES plus(x,s(y)) → s(plus(x,y))plus(x,z) → x,) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_hard
(RULES plus(x,s(y)) → s(plus(x,y))plus(x,z) → x,) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.008 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_hard
(RULES plus(x,s(y)) → s(plus(x,y))plus(x,z) → x,) |
0.01
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y)
Completion of slothrop_hard
(RULES plus(x,s(y)) → s(plus(x,y))plus(x,z) → x,) |
successes | 56 | 85 | 81 | 87 | 90 | 89 |
avg. time | 4.839 | 15.947 | 31.779 | 45.878 | 29.748 | 33.552 |