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
LPO | DPs | DG | DG-2SCC | auto | |
ASK93_1 |
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 time/project: 0 time/sat: 0 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))) |
0.02
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.02 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.006 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))) |
0.03
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.029 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.018 time/project: 0 time/sat: 0.009 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))) |
0.00
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 time/project: 0 time/sat: 0 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 |
0.07
Statisticsiterations: 3 equalities (active): 32 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.046 time/normalization: 0.002 time/overlaps: 0.009 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.009 time/update context: 0.001 Convergent TRS(VAR z)
Completion of ASK93_6
(RULES g(z) → y(b(z))x(h(c(z))) → u(b(c(z)))w(e(f(z))) → h(z)e(y(b(c(z)))) → d(y(b(c(z))))x(w(d(y(z)))) → u(z)o(z) → u(b(c(z)))i(y(b(c(z)))) → e(f(c(z)))x(w(e(y(b(z))))) → x(h(z))x(w(i(z))) → x(w(d(z)))j(f(z)) → z,h(j(z)) → w(e(z))a(z) → i(y(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,) |
0.70
Statisticsiterations: 4 equalities (active): 43 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.653 time/normalization: 0.003 time/overlaps: 0.017 time/orientation constraints: 0.32 time/project: 0 time/sat: 0.228 time/update context: 0.005 Convergent TRS(VAR z)
Completion of ASK93_6
(RULES i(y(z)) → a(z)e(f(c(z))) → i(g(c(z)))x(w(a(z))) → u(z)e(g(c(z))) → d(g(c(z)))w(e(f(z))) → h(z)x(h(c(z))) → o(z)w(i(g(c(z)))) → h(c(z))x(w(e(g(z)))) → x(h(z))x(w(d(y(z)))) → u(z)x(w(d(g(c(z))))) → o(z)u(b(z)) → x(w(d(g(z))))a(b(z)) → i(g(z))x(w(i(z))) → x(w(d(z)))j(f(z)) → z,h(j(z)) → w(e(z))y(b(z)) → g(z)) |
6.27
Statisticsiterations: 5 equalities (active): 57 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 6.181 time/normalization: 0.006 time/overlaps: 0.014 time/orientation constraints: 0.939 time/project: 0 time/sat: 5.049 time/update context: 0.005 Convergent TRS(VAR z)
Completion of ASK93_6
(RULES w(e(z)) → h(j(z))e(f(c(z))) → i(g(c(z)))o(z) → u(b(c(z)))x(w(d(z))) → x(w(i(z)))e(g(c(z))) → d(g(c(z)))x(w(i(y(z)))) → u(z)x(h(c(z))) → u(b(c(z)))w(d(g(c(z)))) → h(j(g(c(z))))w(i(g(c(z)))) → h(c(z))x(w(i(g(z)))) → u(b(z))x(h(j(g(z)))) → x(h(z))j(f(z)) → z,y(b(z)) → g(z)a(z) → i(y(z))) |
0.05
Statisticsiterations: 2 equalities (active): 27 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.029 time/normalization: 0.001 time/overlaps: 0.008 time/orientation constraints: 0.003 time/project: 0 time/sat: 0.008 time/update context: 0 Convergent TRS(VAR z)
Completion of ASK93_6
(RULES w(e(z)) → h(j(z))x(w(d(z))) → x(w(i(z)))o(z) → x(h(c(z)))x(h(j(g(z)))) → x(h(z))i(g(c(z))) → e(f(c(z)))d(g(c(z))) → e(g(c(z)))u(z) → x(w(i(y(z))))j(f(z)) → z,y(b(z)) → g(z)a(z) → i(y(z))) |
BD94_collapse |
0.01
Statisticsiterations: 3 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0.001 time/overlaps: 0 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of BD94_collapse
(RULES a → cb → cf(c,x) → cf(x,c) → x,g(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) |
0.02
Statisticsiterations: 2 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: 0.001 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: 2 equalities (active): 7 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: 0.011 time/project: 0 time/sat: 0.007 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) |
0.01
Statisticsiterations: 2 equalities (active): 7 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 BD94_collapse
(RULES a → bc → bg(x) → x,f(x,b) → x,f(b,x) → b) |
BD94_peano |
0.00
Statisticsiterations: 1 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 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)) |
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 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)) |
0.02
Statisticsiterations: 1 equalities (active): 4 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: 0.002 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: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0 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 |
0.00
Statisticsiterations: 3 equalities (active): 6 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 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) |
0.01
Statisticsiterations: 2 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) |
0.02
Statisticsiterations: 2 equalities (active): 6 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 BD94_sqrt
(RULES sqrt(0) → 0+(0,0) → 0i(0) → 0sqrt(+(i(x),x)) → 0) |
0.00
Statisticsiterations: 2 equalities (active): 6 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 x)
Completion of BD94_sqrt
(RULES sqrt(0) → 0+(0,0) → 0i(0) → 0sqrt(+(i(x),x)) → 0) |
BGK94_D08 |
1.09
Statisticsiterations: 10 equalities (active): 103 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 0.573 time/normalization: 0.266 time/overlaps: 0.118 time/orientation constraints: 0.026 time/project: 0 time/sat: 0.003 time/update context: 0.021 Convergent TRS(VAR x y z)
Completion of BGK94_D08
(RULES f(b,b) → ef(x,i(x)) → ef(x,f(i(x),y)) → y,f(a,f(b,a)) → bf(i(x),x) → ei(b) → bf(a,f(b,f(a,x))) → f(b,x)f(a,f(a,a)) → f(b,f(a,b))f(a,f(a,f(a,x))) → f(b,f(a,f(b,x)))f(a,f(a,b)) → f(b,f(a,a))f(a,f(a,f(b,x))) → f(b,f(a,f(a,x)))i(f(x,y)) → f(i(y),i(x))i(e) → ei(i(x)) → x,i(a) → f(b,f(a,b))f(i(x),f(x,y)) → y,f(e,x) → x,f(b,f(b,x)) → x,f(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,) |
8.10
Statisticsiterations: 10 equalities (active): 117 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 7.769 time/normalization: 0.147 time/overlaps: 0.084 time/orientation constraints: 0.806 time/project: 0 time/sat: 3.137 time/update context: 0.092 Convergent TRS(VAR x y z)
Completion of BGK94_D08
(RULES f(b,b) → ef(x,i(x)) → ef(a,f(b,a)) → bf(i(x),x) → ef(a,f(b,f(a,x))) → f(b,x)i(b) → bf(a,f(a,b)) → f(b,f(a,a))f(a,f(a,f(b,x))) → f(b,f(a,f(a,x)))f(a,f(a,a)) → f(b,f(a,b))i(f(x,y)) → f(i(y),i(x))i(e) → ef(a,f(a,f(a,x))) → f(b,f(a,f(b,x)))i(i(x)) → x,i(a) → f(b,f(a,b))f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,f(e,x) → x,f(b,f(b,x)) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
29.78
Statisticsiterations: 10 equalities (active): 146 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.008 time/maxk: 29.257 time/normalization: 0.191 time/overlaps: 0.123 time/orientation constraints: 2.008 time/project: 0 time/sat: 19.381 time/update context: 0.14 Convergent TRS(VAR x y z)
Completion of BGK94_D08
(RULES f(b,b) → ef(x,i(x)) → ef(i(x),x) → ef(a,f(b,a)) → bi(b) → bf(a,f(b,f(a,x))) → f(b,x)f(a,f(a,f(a,x))) → f(b,f(a,f(b,x)))f(b,f(a,f(a,x))) → f(a,f(a,f(b,x)))i(a) → f(b,f(a,b))f(b,f(a,a)) → f(a,f(a,b))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(a,f(a,a)) → f(b,f(a,b))f(b,f(b,x)) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
10.89
Statisticsiterations: 11 equalities (active): 130 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.013 time/maxk: 10.166 time/normalization: 0.404 time/overlaps: 0.109 time/orientation constraints: 0.021 time/project: 0 time/sat: 0.312 time/update context: 0.21 Convergent TRS(VAR x y z)
Completion of BGK94_D08
(RULES f(b,b) → ef(x,i(x)) → ef(x,f(i(x),y)) → y,f(a,f(a,f(a,x))) → f(b,f(a,f(b,x)))f(a,f(a,a)) → f(b,f(a,b))f(a,f(b,a)) → bf(i(x),x) → ef(a,f(b,f(a,x))) → f(b,x)i(b) → bf(a,f(a,b)) → f(b,f(a,a))f(a,f(a,f(b,x))) → f(b,f(a,f(a,x)))i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,f(i(x),f(x,y)) → y,i(e) → ef(e,x) → x,i(a) → f(b,f(a,b))f(b,f(b,x)) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
BGK94_D10 |
0.84
Statisticsiterations: 10 equalities (active): 114 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 0.434 time/normalization: 0.213 time/overlaps: 0.101 time/orientation constraints: 0.019 time/project: 0 time/sat: 0.002 time/update context: 0.015 Convergent TRS(VAR x y z)
Completion of BGK94_D10
(RULES f(b,b) → ef(x,i(x)) → ef(x,f(i(x),y)) → y,f(a,f(b,a)) → bf(i(x),x) → ei(b) → bf(a,f(b,f(a,x))) → f(b,x)f(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(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,i(e) → ei(i(x)) → x,i(a) → f(b,f(a,b))f(e,x) → x,f(b,f(b,x)) → x,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,) |
20.84
Statisticsiterations: 9 equalities (active): 131 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 20.358 time/normalization: 0.217 time/overlaps: 0.13 time/orientation constraints: 1.03 time/project: 0 time/sat: 12.449 time/update context: 0.14 Convergent TRS(VAR x y z)
Completion of BGK94_D10
(RULES 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,b))))f(b,f(a,x)) → f(a,f(a,f(a,f(a,f(b,x)))))i(e) → ef(e,x) → x,i(a) → f(a,f(a,f(a,a)))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,f(a,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,) |
27.71
Statisticsiterations: 10 equalities (active): 172 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 27.095 time/normalization: 0.24 time/overlaps: 0.156 time/orientation constraints: 1.956 time/project: 0 time/sat: 14.896 time/update context: 0.186 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) → bi(a) → f(a,f(a,f(a,a)))f(b,a) → f(a,f(a,f(a,f(a,b))))f(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) → ef(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,i(i(x)) → x,f(e,x) → x,f(a,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,) |
15.69
Statisticsiterations: 13 equalities (active): 150 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.018 time/maxk: 14.765 time/normalization: 0.535 time/overlaps: 0.19 time/orientation constraints: 0.031 time/project: 0 time/sat: 0.432 time/update context: 0.274 Convergent TRS(VAR x y z)
Completion of BGK94_D10
(RULES f(x,i(x)) → f(b,b)f(x,f(i(x),y)) → y,f(a,f(b,f(a,x))) → f(b,x)f(a,f(b,a)) → bi(b) → bf(a,f(a,a)) → f(b,f(a,f(a,b)))f(a,f(a,f(a,x))) → f(b,f(a,f(a,f(b,x))))f(i(x),x) → f(b,b)f(b,f(b,x)) → x,i(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,i(i(x)) → x,i(a) → f(b,f(a,b))f(x,f(b,b)) → x,f(f(x,y),z) → f(x,f(y,z))e → f(b,b)) |
BGK94_D12 |
129.27
Statisticsiterations: 29 equalities (active): 353 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 12.197 time/maxk: 14.571 time/normalization: 61.075 time/overlaps: 3.468 time/orientation constraints: 0.161 time/project: 0 time/sat: 0.013 time/update context: 0.301 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(e,x) → x,f(x,f(i(x),y)) → y,f(i(x),x) → ei(b) → bf(b,f(a,x)) → f(a,f(a,f(a,f(a,f(a,f(b,x))))))f(b,a) → f(a,f(a,f(a,f(a,f(a,b)))))f(a,f(a,f(a,f(a,f(a,f(a,x)))))) → x,i(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,i(i(x)) → x,i(a) → f(a,f(a,f(a,f(a,a))))i(e) → ef(b,b) → ef(b,f(b,x)) → x,f(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,) |
29.50
Statisticsiterations: 11 equalities (active): 158 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.015 time/maxk: 28.636 time/normalization: 0.411 time/overlaps: 0.221 time/orientation constraints: 1.738 time/project: 0 time/sat: 12.204 time/update context: 0.265 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)) → ei(b) → bf(i(x),x) → ei(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(a,x)) → f(a,f(a,f(a,f(a,f(a,f(b,x))))))f(x,f(i(x),y)) → y,i(f(x,y)) → f(i(y),i(x))f(e,x) → x,i(e) → ei(i(x)) → x,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,x)))))) → x,f(b,b) → ef(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
52.03
Statisticsiterations: 10 equalities (active): 157 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.029 time/maxk: 50.337 time/normalization: 0.996 time/overlaps: 0.246 time/orientation constraints: 2.541 time/project: 0 time/sat: 25.326 time/update context: 0.628 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),f(x,y)) → y,f(i(x),x) → ei(b) → bf(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(a) → f(a,f(a,f(a,f(a,a))))i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,f(x,f(i(x),y)) → y,i(e) → ef(e,x) → x,f(b,f(b,x)) → x,f(a,f(a,f(a,f(a,f(a,f(a,x)))))) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
18.38
Statisticsiterations: 13 equalities (active): 144 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.021 time/maxk: 17.342 time/normalization: 0.634 time/overlaps: 0.198 time/orientation constraints: 0.032 time/project: 0 time/sat: 0.555 time/update context: 0.331 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,f(a,x))) → f(b,x)f(a,f(b,a)) → bf(i(x),x) → ei(b) → bf(a,f(a,f(a,a))) → f(b,f(a,f(a,b)))f(a,f(a,f(a,f(a,x)))) → f(b,f(a,f(a,f(b,x))))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))))i(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,i(e) → ei(i(x)) → x,f(e,x) → x,i(a) → f(b,f(a,b))f(b,f(b,x)) → x,f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
BGK94_D16 |
2.11
Statisticsiterations: 9 equalities (active): 153 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.021 time/maxk: 0.911 time/normalization: 0.766 time/overlaps: 0.278 time/orientation constraints: 0.028 time/project: 0 time/sat: 0.003 time/update context: 0.028 Convergent TRS(VAR x y z)
Completion of BGK94_D16
(RULES f(x,i(x)) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,a)))))))f(i(x),x) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,a)))))))i(b) → bf(a,f(a,f(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,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(a) → f(a,f(a,f(a,f(a,f(a,f(a,a))))))i(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,i(i(x)) → x,f(x,f(i(x),y)) → y,f(b,f(b,x)) → x,f(x,f(a,f(a,f(a,f(a,f(a,f(a,f(a,a)))))))) → x,f(b,b) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,a)))))))f(f(x,y),z) → f(x,f(y,z))e → f(a,f(a,f(a,f(a,f(a,f(a,f(a,a)))))))) |
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,) |
∞ |
35.09
Statisticsiterations: 11 equalities (active): 173 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.017 time/maxk: 33.994 time/normalization: 0.567 time/overlaps: 0.222 time/orientation constraints: 3.419 time/project: 0 time/sat: 16.121 time/update context: 0.256 Convergent TRS(VAR x y z)
Completion of BGK94_D16
(RULES f(b,b) → ef(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(x,f(i(x),y)) → y,i(i(x)) → x,f(i(x),f(x,y)) → y,f(e,x) → x,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(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
46.55
Statisticsiterations: 34 equalities (active): 150 equalities (passive): 0 restarts: 2 time/cache: 0 time/set ops: 0.047 time/maxk: 43.848 time/normalization: 1.743 time/overlaps: 0.491 time/orientation constraints: 1.188 time/project: 0 time/sat: 19.522 time/update context: 0.433 Convergent TRS(VAR x y z)
Completion of BGK94_D16
(RULES f(x,i(x)) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,a)))))))i(b) → bf(i(x),x) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,a)))))))f(b,f(a,x)) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(b,x))))))))f(b,a) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,b)))))))i(a) → f(a,f(a,f(a,f(a,f(a,f(a,a))))))f(a,f(a,f(a,f(a,f(a,f(a,f(a,f(a,x)))))))) → x,i(f(x,y)) → f(i(y),i(x))i(i(x)) → x,e → f(a,f(a,f(a,f(a,f(a,f(a,f(a,a)))))))f(x,f(i(x),y)) → y,f(i(x),f(x,y)) → y,f(b,f(b,x)) → x,f(x,f(a,f(a,f(a,f(a,f(a,f(a,f(a,a)))))))) → x,f(b,b) → f(a,f(a,f(a,f(a,f(a,f(a,f(a,a)))))))f(f(x,y),z) → f(x,f(y,z))) |
BGK94_M08 |
0.26
Statisticsiterations: 6 equalities (active): 97 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.219 time/normalization: 0.008 time/overlaps: 0.017 time/orientation constraints: 0.009 time/project: 0 time/sat: 0.005 time/update context: 0.007 Convergent TRS(VAR x y)
Completion of BGK94_M08
(RULES g(x,y) → f5(y)f2(x) → f5(x)f1(x) → f5(x)f5(j(j(f5(x)))) → f5(x)f5(j(j(j(x)))) → f5(x)f5(j(f5(x))) → f5(j(j(x)))f4(x) → f5(x)f8(x) → f5(x)f6(x) → f5(x)f5(f5(x)) → f5(j(x))f7(x) → f5(x)f3(x) → f5(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)) |
5.23
Statisticsiterations: 7 equalities (active): 116 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.017 time/maxk: 4.912 time/normalization: 0.112 time/overlaps: 0.069 time/orientation constraints: 0.575 time/project: 0 time/sat: 1.272 time/update context: 0.121 Convergent TRS(VAR x y)
Completion of BGK94_M08
(RULES g(x,y) → f1(y)f1(j(x)) → f1(f1(x))f2(x) → f1(x)f1(f1(f1(f1(x)))) → f1(x)f7(x) → f1(x)f8(x) → f1(x)f6(x) → f1(x)f4(x) → f1(x)f5(x) → f1(x)f3(x) → f1(x)) |
11.88
Statisticsiterations: 8 equalities (active): 115 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.012 time/maxk: 11.58 time/normalization: 0.085 time/overlaps: 0.06 time/orientation constraints: 1.114 time/project: 0 time/sat: 7.559 time/update context: 0.092 Convergent TRS(VAR x y)
Completion of BGK94_M08
(RULES g(x,y) → f8(y)f8(j(x)) → f8(f8(x))f2(x) → f8(x)f4(x) → f8(x)f7(x) → f8(x)f1(x) → f8(x)f5(x) → f8(x)f8(f8(f8(f8(x)))) → f8(x)f6(x) → f8(x)f3(x) → f8(x)) |
1.30
Statisticsiterations: 5 equalities (active): 106 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 1.13 time/normalization: 0.062 time/overlaps: 0.043 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.03 time/update context: 0.057 Convergent TRS(VAR x y)
Completion of BGK94_M08
(RULES g(x,y) → f3(y)f1(x) → f3(x)f5(x) → f3(x)f4(x) → f3(x)f3(j(x)) → f3(f3(x))f2(x) → f3(x)f3(f3(f3(f3(x)))) → f3(x)f6(x) → f3(x)f7(x) → f3(x)f8(x) → f3(x)) |
BGK94_M10 |
0.18
Statisticsiterations: 4 equalities (active): 93 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.137 time/normalization: 0.004 time/overlaps: 0.022 time/orientation constraints: 0.007 time/project: 0 time/sat: 0.002 time/update context: 0.004 Convergent TRS(VAR x y)
Completion of BGK94_M10
(RULES g(x,y) → f10(y)f10(j(x)) → f10(f10(x))f9(x) → f10(x)f8(x) → f10(x)f7(x) → f10(x)f2(x) → f10(x)f3(x) → f10(x)f4(x) → f10(x)f5(x) → f10(x)f6(x) → f10(x)f1(x) → f10(x)f10(f10(f10(f10(x)))) → f10(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)) |
8.83
Statisticsiterations: 8 equalities (active): 114 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.028 time/maxk: 8.309 time/normalization: 0.165 time/overlaps: 0.126 time/orientation constraints: 0.699 time/project: 0 time/sat: 3.378 time/update context: 0.165 Convergent TRS(VAR x y)
Completion of BGK94_M10
(RULES g(x,y) → f10(y)f10(j(x)) → f10(f10(x))f9(x) → f10(x)f7(x) → f10(x)f4(x) → f10(x)f1(x) → f10(x)f2(x) → f10(x)f8(x) → f10(x)f10(f10(f10(f10(x)))) → f10(x)f5(x) → f10(x)f6(x) → f10(x)f3(x) → f10(x)) |
30.96
Statisticsiterations: 7 equalities (active): 149 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.024 time/maxk: 30.527 time/normalization: 0.134 time/overlaps: 0.089 time/orientation constraints: 1.033 time/project: 0 time/sat: 25.795 time/update context: 0.14 Convergent TRS(VAR x y)
Completion of BGK94_M10
(RULES g(x,y) → f9(y)f2(x) → f9(x)f6(x) → f9(x)f1(x) → f9(x)f9(j(x)) → f9(f9(x))f3(x) → f9(x)f9(f9(f9(f9(x)))) → f9(x)f10(x) → f9(x)f8(x) → f9(x)f7(x) → f9(x)f4(x) → f9(x)f5(x) → f9(x)) |
0.99
Statisticsiterations: 4 equalities (active): 93 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.018 time/maxk: 0.754 time/normalization: 0.083 time/overlaps: 0.046 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.023 time/update context: 0.05 Convergent TRS(VAR x y)
Completion of BGK94_M10
(RULES g(x,y) → f10(y)f2(x) → f10(x)f9(x) → f10(x)f1(x) → f10(x)f10(j(x)) → f10(f10(x))f5(x) → f10(x)f8(x) → f10(x)f3(x) → f10(x)f6(x) → f10(x)f10(f10(f10(f10(x)))) → f10(x)f7(x) → f10(x)f4(x) → f10(x)) |
BGK94_M12 |
0.19
Statisticsiterations: 4 equalities (active): 96 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 0.144 time/normalization: 0.005 time/overlaps: 0.025 time/orientation constraints: 0.007 time/project: 0 time/sat: 0.002 time/update context: 0.005 Convergent TRS(VAR x y)
Completion of BGK94_M12
(RULES g(x,y) → f12(y)f12(j(x)) → f12(f12(x))f11(x) → f12(x)f10(x) → f12(x)f9(x) → f12(x)f2(x) → f12(x)f3(x) → f12(x)f4(x) → f12(x)f5(x) → f12(x)f6(x) → f12(x)f7(x) → f12(x)f8(x) → f12(x)f1(x) → f12(x)f12(f12(f12(f12(x)))) → f12(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)) |
19.52
Statisticsiterations: 9 equalities (active): 147 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.051 time/maxk: 18.633 time/normalization: 0.3 time/overlaps: 0.224 time/orientation constraints: 0.882 time/project: 0 time/sat: 8.109 time/update context: 0.31 Convergent TRS(VAR x y)
Completion of BGK94_M12
(RULES g(x,y) → f3(y)f8(x) → f3(x)f5(x) → f3(x)f6(x) → f3(x)f1(x) → f3(x)f3(j(x)) → f3(f3(x))f2(x) → f3(x)f3(f3(f3(f3(x)))) → f3(x)f11(x) → f3(x)f4(x) → f3(x)f9(x) → f3(x)f12(x) → f3(x)f7(x) → f3(x)f10(x) → f3(x)) |
25.25
Statisticsiterations: 6 equalities (active): 137 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.044 time/maxk: 24.712 time/normalization: 0.177 time/overlaps: 0.076 time/orientation constraints: 0.693 time/project: 0 time/sat: 20.86 time/update context: 0.156 Convergent TRS(VAR x y)
Completion of BGK94_M12
(RULES g(x,y) → f12(y)f11(x) → f12(x)f3(x) → f12(x)f1(x) → f12(x)f8(x) → f12(x)f5(x) → f12(x)f12(j(x)) → f12(f12(x))f10(x) → f12(x)f2(x) → f12(x)f12(f12(f12(f12(x)))) → f12(x)f7(x) → f12(x)f9(x) → f12(x)f6(x) → f12(x)f4(x) → f12(x)) |
2.71
Statisticsiterations: 6 equalities (active): 116 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.03 time/maxk: 2.311 time/normalization: 0.123 time/overlaps: 0.065 time/orientation constraints: 0.013 time/project: 0 time/sat: 0.06 time/update context: 0.117 Convergent TRS(VAR x y)
Completion of BGK94_M12
(RULES g(x,y) → f2(y)f11(x) → f2(x)f8(x) → f2(x)f1(x) → f2(x)f2(j(x)) → f2(f2(x))f3(x) → f2(x)f4(x) → f2(x)f5(x) → f2(x)f6(x) → f2(x)f7(x) → f2(x)f2(f2(f2(f2(x)))) → f2(x)f12(x) → f2(x)f9(x) → f2(x)f10(x) → f2(x)) |
BGK94_M14 |
0.33
Statisticsiterations: 5 equalities (active): 105 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 0.253 time/normalization: 0.008 time/overlaps: 0.039 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.003 time/update context: 0.009 Convergent TRS(VAR x y)
Completion of BGK94_M14
(RULES g(x,y) → f14(y)f13(x) → f14(x)f6(x) → f14(x)f12(x) → f14(x)f8(x) → f14(x)f11(x) → f14(x)f2(x) → f14(x)f4(x) → f14(x)f5(x) → f14(x)f7(x) → f14(x)f9(x) → f14(x)f1(x) → f14(x)f14(j(x)) → f14(f14(x))f3(x) → f14(x)f14(f14(f14(f14(x)))) → f14(x)f10(x) → f14(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)) |
36.04
Statisticsiterations: 10 equalities (active): 209 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.089 time/maxk: 34.703 time/normalization: 0.415 time/overlaps: 0.314 time/orientation constraints: 1.396 time/project: 0 time/sat: 14.182 time/update context: 0.609 Convergent TRS(VAR x y)
Completion of BGK94_M14
(RULES g(x,y) → f5(y)f6(x) → f5(x)f3(x) → f5(x)f12(x) → f5(x)f11(x) → f5(x)f8(x) → f5(x)f4(x) → f5(x)f5(j(x)) → f5(f5(x))f2(x) → f5(x)f1(x) → f5(x)f5(f5(f5(f5(x)))) → f5(x)f9(x) → f5(x)f10(x) → f5(x)f14(x) → f5(x)f13(x) → f5(x)f7(x) → f5(x)) |
164.53
Statisticsiterations: 11 equalities (active): 256 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.071 time/maxk: 163.316 time/normalization: 0.432 time/overlaps: 0.261 time/orientation constraints: 2.526 time/project: 0 time/sat: 141.531 time/update context: 0.517 Convergent TRS(VAR x y)
Completion of BGK94_M14
(RULES g(x,y) → f11(y)f1(x) → f11(x)f5(x) → f11(x)f3(x) → f11(x)f8(x) → f11(x)f7(x) → f11(x)f4(x) → f11(x)f6(x) → f11(x)f2(x) → f11(x)f10(x) → f11(x)f11(j(x)) → f11(f11(x))f11(f11(f11(f11(x)))) → f11(x)f13(x) → f11(x)f12(x) → f11(x)f14(x) → f11(x)f9(x) → f11(x)) |
3.49
Statisticsiterations: 6 equalities (active): 135 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.052 time/maxk: 2.942 time/normalization: 0.198 time/overlaps: 0.068 time/orientation constraints: 0.014 time/project: 0 time/sat: 0.056 time/update context: 0.151 Convergent TRS(VAR x y)
Completion of BGK94_M14
(RULES g(x,y) → f14(y)f9(x) → f14(x)f12(x) → f14(x)f10(x) → f14(x)f1(x) → f14(x)f14(j(x)) → f14(f14(x))f3(x) → f14(x)f4(x) → f14(x)f5(x) → f14(x)f6(x) → f14(x)f7(x) → f14(x)f8(x) → f14(x)f2(x) → f14(x)f11(x) → f14(x)f13(x) → f14(x)f14(f14(f14(f14(x)))) → f14(x)) |
BH96_fac8_theory |
0.02
Statisticsiterations: 2 equalities (active): 11 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.006 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 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)) → s(+(x,y))*(fac(0),fac(0)) → fac(fac(0))+(x,0) → x,*(x,0) → 0*(x,s(y)) → +(*(x,y),x)) |
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) |
0.06
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.048 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.029 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)) |
0.20
Statisticsiterations: 3 equalities (active): 15 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.181 time/normalization: 0.001 time/overlaps: 0.002 time/orientation constraints: 0.102 time/project: 0 time/sat: 0.066 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)) |
0.01
Statisticsiterations: 1 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.001 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 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))) |
Chr89_A2 |
1.17
Statisticsiterations: 10 equalities (active): 141 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.01 time/maxk: 0.802 time/normalization: 0.139 time/overlaps: 0.125 time/orientation constraints: 0.028 time/project: 0 time/sat: 0.003 time/update context: 0.027 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,) |
29.18
Statisticsiterations: 13 equalities (active): 193 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.014 time/maxk: 28.202 time/normalization: 0.447 time/overlaps: 0.206 time/orientation constraints: 1.763 time/project: 0 time/sat: 4.938 time/update context: 0.333 Convergent TRS(VAR x y z)
Completion of Chr89_A2
(RULES f(x,i2(x)) → a2f(i2(x),a2) → i2(x)f(i2(x),f(x,y)) → y,i2(f(x,y)) → f(i2(y),i2(x))i1(x) → f(i2(x),a1)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,) |
36.39
Statisticsiterations: 13 equalities (active): 219 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.014 time/maxk: 35.23 time/normalization: 0.388 time/overlaps: 0.335 time/orientation constraints: 3.638 time/project: 0 time/sat: 6.524 time/update context: 0.316 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))f(i2(x),f(x,y)) → y,i1(x) → f(i2(x),a1)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,) |
2.19
Statisticsiterations: 9 equalities (active): 115 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 1.979 time/normalization: 0.079 time/overlaps: 0.048 time/orientation constraints: 0.014 time/project: 0 time/sat: 0.073 time/update context: 0.055 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,) |
Chr89_A3 |
6.73
Statisticsiterations: 16 equalities (active): 273 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.041 time/maxk: 5.77 time/normalization: 0.385 time/overlaps: 0.301 time/orientation constraints: 0.085 time/project: 0 time/sat: 0.014 time/update context: 0.149 Convergent TRS(VAR x y z)
Completion of Chr89_A3
(RULES f(x,i1(x)) → a1f(i1(x),a1) → i1(x)i1(f(x,y)) → f(i1(y),i1(x))i3(x) → f(i1(x),a3)i2(x) → f(i1(x),a2)f(i1(x),f(x,y)) → y,i1(i1(x)) → f(x,a1)i1(a3) → a1i1(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,f(a3,x) → x,) |
∞ | ∞ |
586.14
Statisticsiterations: 28 equalities (active): 435 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.092 time/maxk: 582.026 time/normalization: 1.711 time/overlaps: 1.055 time/orientation constraints: 14.183 time/project: 0 time/sat: 250.416 time/update context: 3.861 Convergent TRS(VAR x y z)
Completion of Chr89_A3
(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)i3(x) → f(i1(x),a3)f(i1(x),f(x,y)) → y,i1(i1(x)) → f(x,a1)i1(a3) → a1i1(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,f(a3,x) → x,) |
2.38
Statisticsiterations: 9 equalities (active): 136 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 2.105 time/normalization: 0.097 time/overlaps: 0.078 time/orientation constraints: 0.017 time/project: 0 time/sat: 0.111 time/update context: 0.056 Convergent TRS(VAR x y z)
Completion of Chr89_A3
(RULES f(x,i2(x)) → a2f(i2(x),a2) → i2(x)i2(f(x,y)) → f(i2(y),i2(x))i3(x) → f(i2(x),a3)i1(x) → f(i2(x),a1)i2(i2(x)) → f(x,a2)f(i2(x),f(x,y)) → y,i2(a1) → a2i2(a2) → a2i2(a3) → 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,f(a3,x) → x,) |
KK99_linear_assoc |
0.00
Statisticsiterations: 1 equalities (active): 2 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 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))) |
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: 0.007 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))) |
0.00
Statisticsiterations: 1 equalities (active): 2 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 x y z)
Completion of KK99_linear_assoc
(RULES +(+(x,y),z) → +(x,+(y,z))f(+(x,y)) → +(f(x),f(y))) |
LS06_CGE4 | ∞ |
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))) |
73.15
Statisticsiterations: 8 equalities (active): 129 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.084 time/maxk: 71.16 time/normalization: 0.706 time/overlaps: 0.57 time/orientation constraints: 1.4 time/project: 0 time/sat: 61.081 time/update context: 0.222 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))*(g(x),h(y)) → *(h(y),g(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))*(g(x),*(h(y),z)) → *(h(y),*(g(x),z))*(h(x),*(k(y),z)) → *(k(y),*(h(x),z))*(g(x),*(k(y),z)) → *(k(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)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) → oneh(one) → onek(one) → oneg(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))*(g(x),*(f(y),z)) → *(f(y),*(g(x),z))*(h(x),*(f(y),z)) → *(f(y),*(h(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))) |
159.51
Statisticsiterations: 10 equalities (active): 152 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.062 time/maxk: 156.908 time/normalization: 0.822 time/overlaps: 0.945 time/orientation constraints: 3.139 time/project: 0 time/sat: 140.432 time/update context: 0.337 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))*(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),*(k(y),z)) → *(k(y),*(f(x),z))*(g(x),*(k(y),z)) → *(k(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)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))f(one) → oneh(one) → onek(one) → oneg(one) → onei(one) → onei(i(x)) → x,*(x,one) → x,*(x,i(x)) → one*(i(x),*(x,y)) → y,*(h(x),*(g(y),z)) → *(g(y),*(h(x),z))*(h(x),*(f(y),z)) → *(f(y),*(h(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))*(h(x),f(y)) → *(f(y),h(x))*(h(x),g(y)) → *(g(y),h(x))) |
45.05
Statisticsiterations: 10 equalities (active): 122 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.032 time/maxk: 44.002 time/normalization: 0.333 time/overlaps: 0.283 time/orientation constraints: 0.79 time/project: 0 time/sat: 38.387 time/update context: 0.131 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))*(g(x),h(y)) → *(h(y),g(x))*(f(x),h(y)) → *(h(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))*(f(x),*(g(y),z)) → *(g(y),*(f(x),z))*(f(x),*(h(y),z)) → *(h(y),*(f(x),z))*(g(x),*(h(y),z)) → *(h(y),*(g(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),*(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) → oneh(one) → onek(one) → oneg(one) → onei(one) → onei(i(x)) → x,*(x,one) → x,*(x,i(x)) → one*(i(x),*(x,y)) → y,*(one,x) → x,*(i(x),x) → one*(*(x,y),z) → *(x,*(y,z))) |
LS06_CGE5 | ∞ |
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))) |
155.47
Statisticsiterations: 10 equalities (active): 159 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.102 time/maxk: 152.389 time/normalization: 1.062 time/overlaps: 0.848 time/orientation constraints: 1.894 time/project: 0 time/sat: 135.916 time/update context: 0.453 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))*(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),*(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))*(g(x),*(k(y),z)) → *(k(y),*(g(x),z))*(h(x),*(k(y),z)) → *(k(y),*(h(x),z))*(j(x),*(h(y),z)) → *(h(y),*(j(x),z))*(j(x),*(g(y),z)) → *(g(y),*(j(x),z))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,*(j(x),*(k(y),z)) → *(k(y),*(j(x),z))*(j(x),*(f(y),z)) → *(f(y),*(j(x),z))*(k(x),*(f(y),z)) → *(f(y),*(k(x),z))*(h(x),*(f(y),z)) → *(f(y),*(h(x),z))*(g(x),*(f(y),z)) → *(f(y),*(g(x),z))*(h(x),*(g(y),z)) → *(g(y),*(h(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))*(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))) |
254.04
Statisticsiterations: 10 equalities (active): 162 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.231 time/maxk: 248.14 time/normalization: 2.034 time/overlaps: 1.76 time/orientation constraints: 4.51 time/project: 0 time/sat: 225.547 time/update context: 0.591 Convergent TRS(VAR x y z)
Completion of LS06_CGE5
(RULES *(g(x),k(y)) → *(k(y),g(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))*(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),*(k(y),z)) → *(k(y),*(g(x),z))*(g(x),*(h(y),z)) → *(h(y),*(g(x),z))*(f(x),*(h(y),z)) → *(h(y),*(f(x),z))*(f(x),*(k(y),z)) → *(k(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))*(j(x),*(k(y),z)) → *(k(y),*(j(x),z))*(x,*(i(x),y)) → y,i(*(x,y)) → *(i(y),i(x))g(one) → oneh(one) → onek(one) → onej(one) → onef(one) → onei(one) → onei(i(x)) → x,*(x,one) → x,*(x,i(x)) → one*(i(x),*(x,y)) → y,*(k(x),*(h(y),z)) → *(h(y),*(k(x),z))*(g(x),*(f(y),z)) → *(f(y),*(g(x),z))*(j(x),*(h(y),z)) → *(h(y),*(j(x),z))*(j(x),*(f(y),z)) → *(f(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))*(g(x),f(y)) → *(f(y),g(x))*(k(x),h(y)) → *(h(y),k(x))*(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))) |
104.41
Statisticsiterations: 11 equalities (active): 149 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.069 time/maxk: 102.39 time/normalization: 0.69 time/overlaps: 0.753 time/orientation constraints: 1.064 time/project: 0 time/sat: 93.15 time/update context: 0.253 Convergent TRS(VAR x y z)
Completion of LS06_CGE5
(RULES *(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),*(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(k(x)) → k(i(x))i(g(x)) → g(i(x))i(f(x)) → f(i(x))i(h(x)) → h(i(x))*(j(x),*(h(y),z)) → *(h(y),*(j(x),z))i(*(x,y)) → *(i(y),i(x))*(x,*(i(x),y)) → y,f(one) → oneh(one) → onek(one) → onej(one) → oneg(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),*(f(y),z)) → *(f(y),*(k(x),z))*(h(x),*(g(y),z)) → *(g(y),*(h(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))*(j(x),*(k(y),z)) → *(k(y),*(j(x),z))*(j(x),*(f(y),z)) → *(f(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))*(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),h(y)) → *(h(y),k(x))*(k(x),g(y)) → *(g(y),k(x))*(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))) |
LS94_G0 |
0.09
Statisticsiterations: 4 equalities (active): 35 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.023 time/normalization: 0.019 time/overlaps: 0.029 time/orientation constraints: 0.005 time/project: 0 time/sat: 0 time/update context: 0.003 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,) |
0.75
Statisticsiterations: 4 equalities (active): 53 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.575 time/normalization: 0.048 time/overlaps: 0.084 time/orientation constraints: 0.124 time/project: 0 time/sat: 0.087 time/update context: 0.009 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,) |
0.58
Statisticsiterations: 4 equalities (active): 53 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.451 time/normalization: 0.04 time/overlaps: 0.051 time/orientation constraints: 0.155 time/project: 0 time/sat: 0.09 time/update context: 0.006 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,) |
0.14
Statisticsiterations: 4 equalities (active): 35 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.086 time/normalization: 0.013 time/overlaps: 0.024 time/orientation constraints: 0.002 time/project: 0 time/sat: 0.007 time/update context: 0.005 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 |
4.90
Statisticsiterations: 17 equalities (active): 228 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.095 time/maxk: 3.14 time/normalization: 0.759 time/overlaps: 0.347 time/orientation constraints: 0.201 time/project: 0 time/sat: 0.015 time/update context: 0.078 Convergent TRS(VAR x y z)
Completion of LS94_P1
(RULES f(i(x),x) → ef(x,i(x)) → eS(x) → x,R(x) → x,t(x) → x,r(x) → x,T(x) → x,s(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,) |
∞ | ∞ | ∞ |
151.62
Statisticsiterations: 22 equalities (active): 337 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.088 time/maxk: 148.447 time/normalization: 1.758 time/overlaps: 0.696 time/orientation constraints: 0.415 time/project: 0 time/sat: 41.654 time/update context: 4.477 Convergent TRS(VAR x y z)
Completion of LS94_P1
(RULES f(i(x),x) → ef(x,i(x)) → eT(x) → x,r(x) → x,R(x) → x,S(x) → x,t(x) → x,s(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 |
0.01
Statisticsiterations: 1 equalities (active): 9 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0 time/project: 0 time/sat: 0 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))) |
0.04
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: 0.003 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))) |
2.57
Statisticsiterations: 5 equalities (active): 65 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 2.382 time/normalization: 0.042 time/overlaps: 0.037 time/orientation constraints: 1.2 time/project: 0 time/sat: 0.652 time/update context: 0.011 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))) |
0.01
Statisticsiterations: 1 equalities (active): 9 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.001 time/normalization: 0 time/overlaps: 0.003 time/orientation constraints: 0 time/project: 0 time/sat: 0 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 |
0.01
Statisticsiterations: 1 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0.004 time/orientation constraints: 0 time/project: 0 time/sat: 0 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)) |
0.04
Statisticsiterations: 1 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.027 time/normalization: 0 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 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)) |
10.74
Statisticsiterations: 4 equalities (active): 80 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 10.589 time/normalization: 0.009 time/overlaps: 0.031 time/orientation constraints: 0.867 time/project: 0 time/sat: 9.469 time/update context: 0.013 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,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) → ffhas(+(x,y),u) → if(eq(y,u),eq(0,0),has(x,u))subset(empty,x) → eq(0,0)subset(+(x,y),u) → if(has(u,y),subset(x,u),ff)) |
0.02
Statisticsiterations: 1 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0 time/overlaps: 0.003 time/orientation constraints: 0 time/project: 0 time/sat: 0 time/update context: 0.001 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)) |
OKW95_dt1_theory | ∞ | ∞ | ∞ |
426.30
Statisticsiterations: 34 equalities (active): 259 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.05 time/maxk: 419.245 time/normalization: 5.57 time/overlaps: 0.338 time/orientation constraints: 171.502 time/project: 0 time/sat: 191.188 time/update context: 1.392 Convergent TRS(VAR x y)
Completion of OKW95_dt1_theory
(RULES -(x,s(0)) → p(x)fib(s(s(x))) → +(fib(s(x)),fib(x))p(s(x)) → x,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,) |
36.19
Statisticsiterations: 21 equalities (active): 291 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.04 time/maxk: 33.796 time/normalization: 1.744 time/overlaps: 0.326 time/orientation constraints: 0.349 time/project: 0 time/sat: 0.202 time/update context: 1.044 Convergent TRS(VAR x y)
Completion of OKW95_dt1_theory
(RULES -(x,s(0)) → p(x)fib(s(s(x))) → +(fib(s(x)),fib(x))p(s(x)) → x,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 |
0.27
Statisticsiterations: 6 equalities (active): 80 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 0.102 time/normalization: 0.078 time/overlaps: 0.048 time/orientation constraints: 0.008 time/project: 0 time/sat: 0 time/update context: 0.007 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))) |
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))) |
300.35
Statisticsiterations: 19 equalities (active): 292 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.077 time/maxk: 292.116 time/normalization: 5.699 time/overlaps: 1.397 time/orientation constraints: 6.414 time/project: 0 time/sat: 145.9 time/update context: 2.458 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))) |
237.65
Statisticsiterations: 32 equalities (active): 212 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.086 time/maxk: 222.371 time/normalization: 11.525 time/overlaps: 1.653 time/orientation constraints: 11.1 time/project: 0 time/sat: 109.871 time/update context: 1.59 Convergent TRS(VAR y x z)
Completion of SK90_3.01
(RULES *(y,i(y)) → onei(*(y,x)) → *(i(x),i(y))i(one) → onei(i(y)) → y,*(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))) |
0.50
Statisticsiterations: 6 equalities (active): 69 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.379 time/normalization: 0.05 time/overlaps: 0.037 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.029 time/update context: 0.014 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 |
0.00
Statisticsiterations: 1 equalities (active): 3 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 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))) |
0.02
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0.001 time/overlaps: 0 time/orientation constraints: 0.011 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: 0.01 time/normalization: 0.001 time/overlaps: 0 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.001 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))) |
0.00
Statisticsiterations: 1 equalities (active): 3 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 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 | ∞ |
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) |
2.54
Statisticsiterations: 5 equalities (active): 113 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 2.253 time/normalization: 0.093 time/overlaps: 0.112 time/orientation constraints: 0.524 time/project: 0 time/sat: 0.355 time/update context: 0.049 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) |
3.77
Statisticsiterations: 5 equalities (active): 120 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 3.417 time/normalization: 0.099 time/overlaps: 0.116 time/orientation constraints: 0.895 time/project: 0 time/sat: 1.134 time/update context: 0.044 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) |
2.04
Statisticsiterations: 9 equalities (active): 98 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.004 time/maxk: 1.789 time/normalization: 0.081 time/overlaps: 0.083 time/orientation constraints: 0.254 time/project: 0 time/sat: 0.606 time/update context: 0.033 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,x),z) → *(y,*(x,z))*(y,*(i(y),x)) → x,*(y,one) → y,*(y,i(y)) → one*(i(y),*(y,x)) → x,i(one) → one*(one,y) → y,*(i(y),y) → one) |
SK90_3.04 |
1.31
Statisticsiterations: 9 equalities (active): 113 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.03 time/maxk: 0.304 time/normalization: 0.41 time/overlaps: 0.228 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.003 time/update context: 0.012 Convergent TRS(VAR x y z)
Completion of SK90_3.04
(RULES *(f(x),x) → g(x)*(f(*(x,y)),z) → *(f(y),*(f(x),z))g(*(x,y)) → g(y)g(one) → one*(x,g(x)) → x,g(g(x)) → g(x)g(f(x)) → *(x,f(x))*(x,*(f(x),y)) → y,*(f(one),x) → x,*(f(g(x)),y) → y,*(f(f(x)),y) → *(x,y)*(f(x),*(x,y)) → y,*(*(x,y),z) → *(x,*(y,z))*(one,x) → x,*(g(x),y) → y,) |
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)) |
57.05
Statisticsiterations: 10 equalities (active): 146 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.052 time/maxk: 54.406 time/normalization: 1.147 time/overlaps: 0.561 time/orientation constraints: 0.891 time/project: 0 time/sat: 36.618 time/update context: 0.244 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)) |
41.61
Statisticsiterations: 11 equalities (active): 166 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.052 time/maxk: 39.575 time/normalization: 0.852 time/overlaps: 0.391 time/orientation constraints: 1.559 time/project: 0 time/sat: 20.192 time/update context: 0.235 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)) |
1.36
Statisticsiterations: 7 equalities (active): 76 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.015 time/maxk: 0.978 time/normalization: 0.14 time/overlaps: 0.101 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.031 time/update context: 0.016 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 |
2.29
Statisticsiterations: 11 equalities (active): 169 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.01 time/maxk: 1.277 time/normalization: 0.404 time/overlaps: 0.199 time/orientation constraints: 0.017 time/project: 0 time/sat: 0.002 time/update context: 0.038 Convergent TRS(VAR y x z)
Completion of SK90_3.05
(RULES *(y,g(y)) → g(y)*(f(y),y) → f(y)f(g(y)) → g(y)*(y,*(x,z)) → *(y,g(x))*(y,f(x)) → *(y,x)*(*(y,x),z) → *(f(x),z)f(*(y,x)) → g(y)g(*(y,x)) → f(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)) |
∞ | ∞ | ∞ |
22.06
Statisticsiterations: 33 equalities (active): 155 equalities (passive): 0 restarts: 2 time/cache: 0 time/set ops: 0.024 time/maxk: 15.533 time/normalization: 0.958 time/overlaps: 0.661 time/orientation constraints: 0.561 time/project: 0 time/sat: 1.038 time/update context: 0.324 Convergent TRS(VAR y x z)
Completion of SK90_3.05
(RULES *(f(y),y) → f(y)*(y,g(y)) → g(y)f(g(y)) → g(y)*(y,*(x,z)) → *(y,g(x))*(y,f(x)) → *(y,x)*(*(y,x),z) → *(f(x),z)f(*(y,x)) → g(y)g(*(y,x)) → f(x)f(f(y)) → f(y)g(g(y)) → g(y)g(f(y)) → f(y)*(f(y),g(y)) → y,*(g(y),x) → *(y,x)) |
SK90_3.06 |
0.59
Statisticsiterations: 8 equalities (active): 118 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.008 time/maxk: 0.298 time/normalization: 0.109 time/overlaps: 0.103 time/orientation constraints: 0.012 time/project: 0 time/sat: 0.001 time/update context: 0.012 Convergent TRS(VAR x y z)
Completion of SK90_3.06
(RULES *(x,i(x)) → 1*(x,*(i(x),y)) → y,*(i(x),x) → 1f(x,y) → g(x,*(i(y),x))i(*(x,y)) → *(i(y),i(x))g(1,x) → i(x)*(i(x),*(x,y)) → y,i(1) → 1i(i(x)) → x,*(1,x) → x,*(x,1) → x,*(*(x,y),z) → *(x,*(y,z))) |
∞ | ∞ | ∞ |
2.16
Statisticsiterations: 9 equalities (active): 105 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 1.885 time/normalization: 0.13 time/overlaps: 0.075 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.067 time/update context: 0.069 Convergent TRS(VAR x y z)
Completion of SK90_3.06
(RULES *(x,i(x)) → 1*(x,*(i(x),y)) → y,f(x,y) → g(x,*(i(y),x))*(i(x),x) → 1i(*(x,y)) → *(i(y),i(x))g(1,x) → i(x)*(i(x),*(x,y)) → y,i(1) → 1i(i(x)) → x,*(1,x) → x,*(x,1) → x,*(*(x,y),z) → *(x,*(y,z))) |
SK90_3.07 |
0.47
Statisticsiterations: 8 equalities (active): 104 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 0.198 time/normalization: 0.116 time/overlaps: 0.091 time/orientation constraints: 0.009 time/project: 0 time/sat: 0 time/update context: 0.009 Convergent TRS(VAR x y z)
Completion of SK90_3.07
(RULES +(x,-(x)) → 0+(x,+(-(x),y)) → y,+(-(x),x) → 0-(+(x,y)) → +(-(y),-(x))g(x,y) → f(x,+(x,-(y)),y)+(-(x),+(x,y)) → y,-(0) → 0-(-(x)) → x,+(0,x) → x,+(x,0) → 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,) |
11.27
Statisticsiterations: 10 equalities (active): 132 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.014 time/maxk: 10.551 time/normalization: 0.326 time/overlaps: 0.174 time/orientation constraints: 1.319 time/project: 0 time/sat: 1.961 time/update context: 0.222 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,) |
7.83
Statisticsiterations: 10 equalities (active): 135 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 7.294 time/normalization: 0.19 time/overlaps: 0.169 time/orientation constraints: 1.409 time/project: 0 time/sat: 1.835 time/update context: 0.149 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,) |
3.67
Statisticsiterations: 10 equalities (active): 120 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.008 time/maxk: 3.27 time/normalization: 0.21 time/overlaps: 0.097 time/orientation constraints: 0.013 time/project: 0 time/sat: 0.057 time/update context: 0.123 Convergent TRS(VAR x y z)
Completion of SK90_3.07
(RULES +(x,-(x)) → 0+(x,+(-(x),y)) → y,+(-(x),x) → 0-(+(x,y)) → +(-(y),-(x))g(x,y) → f(x,+(x,-(y)),y)+(-(x),+(x,y)) → y,-(0) → 0+(0,x) → x,+(x,0) → x,-(-(x)) → x,+(+(x,y),z) → +(x,+(y,z))f(0,x,y) → x,) |
SK90_3.08 |
0.01
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0 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: 0.012 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,) |
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: 0.003 time/orientation constraints: 0.003 time/project: 0 time/sat: 0.003 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,) |
0.04
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.028 time/normalization: 0 time/overlaps: 0.003 time/orientation constraints: 0.011 time/project: 0 time/sat: 0.007 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,) |
0.01
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0 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,) |
SK90_3.10 |
0.01
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR 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,) |
0.01
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0.004 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: 0.005 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 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: 0.001 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0 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 |
0.01
Statisticsiterations: 3 equalities (active): 10 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 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,) |
0.13
Statisticsiterations: 3 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.114 time/normalization: 0 time/overlaps: 0.004 time/orientation constraints: 0.081 time/project: 0 time/sat: 0.006 time/update context: 0.003 Convergent TRS(VAR x)
Completion of SK90_3.11
(RULES p(x) → x,s(x) → x,+(x,0) → x,) |
0.05
Statisticsiterations: 3 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.042 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.031 time/project: 0 time/sat: 0.005 time/update context: 0 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): 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 time/project: 0 time/sat: 0 time/update context: 0 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 |
0.02
Statisticsiterations: 2 equalities (active): 12 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 time/normalization: 0.003 time/overlaps: 0.006 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.13
(RULES *(x,*(1,y)) → *(x,y)+(x,+(0,y)) → +(x,y)+(+(x,y),z) → +(x,+(y,z))+(x,0) → x,*(*(x,y),z) → *(x,*(y,z))*(x,1) → x,exp(0) → 1exp(+(x,y)) → *(exp(x),exp(y))) |
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))) |
0.03
Statisticsiterations: 1 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.021 time/normalization: 0.002 time/overlaps: 0.002 time/orientation constraints: 0.014 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))) |
0.17
Statisticsiterations: 2 equalities (active): 15 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.14 time/normalization: 0.009 time/overlaps: 0.004 time/orientation constraints: 0.089 time/project: 0 time/sat: 0.038 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))) |
0.05
Statisticsiterations: 2 equalities (active): 15 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.011 time/normalization: 0.002 time/overlaps: 0.004 time/orientation constraints: 0 time/project: 0 time/sat: 0.004 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.13
(RULES 1 → exp(0)+(x,+(0,y)) → +(x,y)*(x,exp(0)) → x,*(x,*(exp(0),y)) → *(x,y)+(+(x,y),z) → +(x,+(y,z))+(x,0) → x,*(*(x,y),z) → *(x,*(y,z))exp(+(x,y)) → *(exp(x),exp(y))) |
SK90_3.14 |
0.02
Statisticsiterations: 2 equalities (active): 15 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.008 time/normalization: 0.001 time/overlaps: 0.006 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 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)) |
∞ |
0.27
Statisticsiterations: 3 equalities (active): 40 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.222 time/normalization: 0.011 time/overlaps: 0.007 time/orientation constraints: 0.122 time/project: 0 time/sat: 0.035 time/update context: 0.003 Convergent TRS(VAR x y)
Completion of SK90_3.14
(RULES f(x,0) → g(h(0),x)s(x) → f(h(0),x)g(f(h(0),x),y) → g(h(0),g(x,y))g(h(0),h(0)) → h(0)f(f(h(0),x),y) → f(h(0),f(x,y))f(h(0),h(0)) → 0f(h(0),f(h(0),x)) → x,g(h(0),0) → 0g(h(0),g(h(0),x)) → x,g(h(0),f(h(0),x)) → f(h(0),g(h(0),x))f(0,x) → x,g(0,x) → x,) |
∞ |
0.02
Statisticsiterations: 2 equalities (active): 15 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.01 time/normalization: 0 time/overlaps: 0.003 time/orientation constraints: 0.001 time/project: 0 time/sat: 0.002 time/update context: 0 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)) |
SK90_3.15 | ∞ |
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)) |
0.05
Statisticsiterations: 2 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.033 time/normalization: 0 time/overlaps: 0.005 time/orientation constraints: 0.022 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)) |
0.07
Statisticsiterations: 2 equalities (active): 10 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.052 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.032 time/project: 0 time/sat: 0.013 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)) |
0.32
Statisticsiterations: 14 equalities (active): 10 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0 time/maxk: 0.221 time/normalization: 0.033 time/overlaps: 0.028 time/orientation constraints: 0.012 time/project: 0 time/sat: 0.004 time/update context: 0.006 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 |
0.00
Statisticsiterations: 2 equalities (active): 5 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 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: 0.003 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 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: 0.007 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_3.16
(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 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 |
0.01
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.001 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 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,) |
0.04
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.024 time/normalization: 0.001 time/overlaps: 0.002 time/orientation constraints: 0.016 time/project: 0 time/sat: 0.004 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: 0.043 time/normalization: 0.001 time/overlaps: 0.002 time/orientation constraints: 0.032 time/project: 0 time/sat: 0.007 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,) |
0.01
Statisticsiterations: 2 equalities (active): 6 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0.001 time/overlaps: 0.002 time/orientation constraints: 0 time/project: 0 time/sat: 0 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 |
0.03
Statisticsiterations: 3 equalities (active): 14 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.012 time/normalization: 0.002 time/overlaps: 0.005 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 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,) |
0.38
Statisticsiterations: 3 equalities (active): 24 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.348 time/normalization: 0.008 time/overlaps: 0.008 time/orientation constraints: 0.236 time/project: 0 time/sat: 0.071 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,) |
0.47
Statisticsiterations: 3 equalities (active): 24 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.434 time/normalization: 0.001 time/overlaps: 0.003 time/orientation constraints: 0.239 time/project: 0 time/sat: 0.165 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,) |
0.02
Statisticsiterations: 3 equalities (active): 15 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.012 time/normalization: 0 time/overlaps: 0.003 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 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,) |
SK90_3.19 |
0.03
Statisticsiterations: 2 equalities (active): 20 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.018 time/normalization: 0.003 time/overlaps: 0.006 time/orientation constraints: 0.003 time/project: 0 time/sat: 0.001 time/update context: 0 Convergent TRS(VAR y x z)
Completion of SK90_3.19
(RULES @(.(y,x),z) → .(y,@(x,z))@(rev(y),nil) → rev(y)@(nil,y) → y,@(@(y,x),z) → @(y,@(x,z))rev(nil) → nilrev(.(y,x)) → @(rev(x),.(y,nil))reviter(y,x) → @(rev(y),x)) |
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)) |
12.17
Statisticsiterations: 10 equalities (active): 123 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.012 time/maxk: 10.749 time/normalization: 0.578 time/overlaps: 0.409 time/orientation constraints: 4.483 time/project: 0 time/sat: 1.225 time/update context: 0.159 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)) |
0.24
Statisticsiterations: 2 equalities (active): 26 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.215 time/normalization: 0.002 time/overlaps: 0.004 time/orientation constraints: 0.126 time/project: 0 time/sat: 0.069 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)) |
0.03
Statisticsiterations: 2 equalities (active): 23 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: 0.001 time/project: 0 time/sat: 0.002 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)) |
SK90_3.20 |
0.05
Statisticsiterations: 2 equalities (active): 30 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.021 time/normalization: 0.001 time/overlaps: 0.014 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0.002 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)) → falseeq(x,x) → trueand(true,true) → 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) |
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) |
4.68
Statisticsiterations: 8 equalities (active): 131 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 4.191 time/normalization: 0.072 time/overlaps: 0.131 time/orientation constraints: 1.913 time/project: 0 time/sat: 0.706 time/update context: 0.055 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) |
11.71
Statisticsiterations: 8 equalities (active): 149 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 11.107 time/normalization: 0.041 time/overlaps: 0.171 time/orientation constraints: 4.099 time/project: 0 time/sat: 5.59 time/update context: 0.047 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) |
0.06
Statisticsiterations: 2 equalities (active): 30 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.021 time/normalization: 0.001 time/overlaps: 0.015 time/orientation constraints: 0.001 time/project: 0 time/sat: 0.002 time/update context: 0.001 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 |
0.15
Statisticsiterations: 3 equalities (active): 69 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.048 time/normalization: 0.038 time/overlaps: 0.027 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0.002 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) |
1.16
Statisticsiterations: 3 equalities (active): 71 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 0.923 time/normalization: 0.083 time/overlaps: 0.063 time/orientation constraints: 0.47 time/project: 0 time/sat: 0.058 time/update context: 0.025 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) |
0.82
Statisticsiterations: 3 equalities (active): 73 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.719 time/normalization: 0.029 time/overlaps: 0.022 time/orientation constraints: 0.398 time/project: 0 time/sat: 0.138 time/update context: 0.01 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) |
0.32
Statisticsiterations: 3 equalities (active): 78 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.225 time/normalization: 0.036 time/overlaps: 0.03 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.002 time/update context: 0.015 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) |
SK90_3.22 |
3.35
Statisticsiterations: 13 equalities (active): 226 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.02 time/maxk: 3.184 time/normalization: 0.071 time/overlaps: 0.035 time/orientation constraints: 0.101 time/project: 0 time/sat: 0.009 time/update context: 0.055 Convergent TRS(VAR x)
Completion of SK90_3.22
(RULES e(x) → c(c(c(c(c(c(c(c(c(x)))))))))b(x) → c(c(c(c(x))))a(x) → c(c(c(c(c(x)))))d(x) → c(c(c(x)))c(c(c(c(c(c(c(c(c(c(c(c(x)))))))))))) → c(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))) |
301.06
Statisticsiterations: 18 equalities (active): 372 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.101 time/maxk: 297.075 time/normalization: 3.332 time/overlaps: 0.117 time/orientation constraints: 10.422 time/project: 0 time/sat: 134.776 time/update context: 4.523 Convergent TRS(VAR x)
Completion of SK90_3.22
(RULES d(d(d(x))) → a(a(a(a(x))))e(x) → a(a(a(a(x))))d(a(a(a(a(x))))) → c(x)d(c(x)) → a(a(a(x)))d(d(a(a(x)))) → a(x)c(a(x)) → d(d(x))a(a(a(a(a(x))))) → d(x)b(x) → a(a(a(x)))a(d(x)) → d(a(x))c(d(x)) → a(a(a(x)))a(c(x)) → d(d(x))c(c(x)) → d(a(a(x)))) |
∞ |
19.63
Statisticsiterations: 13 equalities (active): 226 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.032 time/maxk: 18.682 time/normalization: 0.801 time/overlaps: 0.044 time/orientation constraints: 0.096 time/project: 0 time/sat: 0.264 time/update context: 0.743 Convergent TRS(VAR x)
Completion of SK90_3.22
(RULES d(x) → b(b(b(b(b(b(b(b(b(x)))))))))a(x) → b(b(b(b(x))))e(x) → b(b(b(b(b(x)))))b(b(b(b(b(b(b(b(b(b(b(b(x)))))))))))) → b(x)c(x) → b(b(b(x)))) |
SK90_3.23 |
0.32
Statisticsiterations: 20 equalities (active): 61 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.001 time/maxk: 0.238 time/normalization: 0.013 time/overlaps: 0.04 time/orientation constraints: 0.024 time/project: 0 time/sat: 0.003 time/update context: 0.01 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(a(x)) → a(c(x))c(d(a(x))) → a(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)) |
0.18
Statisticsiterations: 4 equalities (active): 24 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.153 time/normalization: 0.002 time/overlaps: 0.007 time/orientation constraints: 0.084 time/project: 0 time/sat: 0.024 time/update context: 0.002 Convergent TRS(VAR x)
Completion of SK90_3.23
(RULES e(c(x)) → a(x)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))c(e(x)) → a(x)b(d(x)) → x,) |
0.33
Statisticsiterations: 5 equalities (active): 23 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.304 time/normalization: 0.001 time/overlaps: 0.005 time/orientation constraints: 0.178 time/project: 0 time/sat: 0.077 time/update context: 0.001 Convergent TRS(VAR x)
Completion of SK90_3.23
(RULES e(c(x)) → a(x)d(a(x)) → e(x)e(a(x)) → a(e(x))b(e(x)) → a(x)b(a(x)) → a(c(x))c(e(x)) → a(x)c(a(x)) → a(c(x))b(d(x)) → x,) |
0.03
Statisticsiterations: 3 equalities (active): 32 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.022 time/normalization: 0 time/overlaps: 0.003 time/orientation constraints: 0.002 time/project: 0 time/sat: 0.001 time/update context: 0.001 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(d(a(x))) → a(x)c(a(x)) → a(c(x))b(d(x)) → x,e(x) → d(a(x))) |
SK90_3.24 |
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 time/orientation constraints: 0 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.24
(RULES b(x) → a(x)a(a(a(x))) → a(a(x))c(x) → a(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)) |
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: 0.006 time/project: 0 time/sat: 0.003 time/update context: 0.001 Convergent TRS(VAR x)
Completion of SK90_3.24
(RULES a(x) → c(x)c(c(c(x))) → c(c(x))b(x) → c(x)) |
0.03
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.028 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.019 time/project: 0 time/sat: 0.005 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)) |
0.01
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 time/orientation constraints: 0 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.24
(RULES a(x) → c(x)c(c(c(x))) → c(c(x))b(x) → c(x)) |
SK90_3.25 |
0.01
Statisticsiterations: 2 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 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)) |
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: 0.009 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)) |
0.03
Statisticsiterations: 2 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.028 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.024 time/project: 0 time/sat: 0.002 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)) |
0.00
Statisticsiterations: 2 equalities (active): 2 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 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 |
4.13
Statisticsiterations: 13 equalities (active): 228 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.034 time/maxk: 3.762 time/normalization: 0.168 time/overlaps: 0.093 time/orientation constraints: 0.166 time/project: 0 time/sat: 0.009 time/update context: 0.063 Convergent TRS(VAR x)
Completion of SK90_3.26
(RULES u(x) → a(a(a(a(a(a(x))))))c(a(c(x))) → a(a(c(a(x))))c(a(a(a(c(x))))) → a(c(a(a(a(a(x))))))c(a(a(a(a(a(c(x))))))) → a(a(x))c(a(a(a(a(c(x)))))) → a(a(a(a(c(a(a(x)))))))c(c(x)) → a(a(a(c(a(a(a(a(a(a(x))))))))))b(x) → a(a(a(a(c(a(a(a(a(a(x))))))))))c(a(a(a(a(a(a(c(x)))))))) → a(a(a(a(a(c(a(a(a(x)))))))))c(a(a(c(x)))) → a(a(a(a(a(a(c(a(a(a(a(a(x))))))))))))a(a(a(a(a(a(a(x))))))) → x,w(x) → a(a(a(a(a(c(a(a(a(a(a(x)))))))))))v(x) → c(a(x))) |
∞ | ∞ | ∞ | ∞ |
SK90_3.27 |
0.95
Statisticsiterations: 6 equalities (active): 128 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.023 time/maxk: 0.791 time/normalization: 0.067 time/overlaps: 0.031 time/orientation constraints: 0.077 time/project: 0 time/sat: 0.003 time/update context: 0.02 Convergent TRS(VAR x)
Completion of SK90_3.27
(RULES c(x) → x,a(x) → x,b(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,) |
6.80
Statisticsiterations: 5 equalities (active): 106 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.04 time/maxk: 6.25 time/normalization: 0.305 time/overlaps: 0.038 time/orientation constraints: 1.444 time/project: 0 time/sat: 0.925 time/update context: 0.202 Convergent TRS(VAR x)
Completion of SK90_3.27
(RULES c(x) → x,b(x) → x,a(x) → x,) |
7.78
Statisticsiterations: 5 equalities (active): 109 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.031 time/maxk: 7.295 time/normalization: 0.234 time/overlaps: 0.035 time/orientation constraints: 2.151 time/project: 0 time/sat: 2.629 time/update context: 0.169 Convergent TRS(VAR x)
Completion of SK90_3.27
(RULES b(x) → x,a(x) → x,c(x) → x,) |
6.99
Statisticsiterations: 7 equalities (active): 133 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.03 time/maxk: 6.623 time/normalization: 0.258 time/overlaps: 0.024 time/orientation constraints: 0.057 time/project: 0 time/sat: 0.053 time/update context: 0.593 Convergent TRS(VAR x)
Completion of SK90_3.27
(RULES c(x) → x,a(x) → x,b(x) → x,) |
SK90_3.28 | ∞ |
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,) |
∞ | ∞ |
4.56
Statisticsiterations: 9 equalities (active): 157 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.012 time/maxk: 4.398 time/normalization: 0.079 time/overlaps: 0.031 time/orientation constraints: 0.027 time/project: 0 time/sat: 0.222 time/update context: 0.18 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(c(x)) → w(a(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 |
0.05
Statisticsiterations: 3 equalities (active): 27 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.03 time/normalization: 0.002 time/overlaps: 0.009 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.004 time/update context: 0 Convergent TRS(VAR x)
Completion of SK90_3.29
(RULES c(w(x)) → u(x)a(u(x)) → b(u(x))a(d(x)) → v(a(x))a(c(x)) → e(a(x))e(b(w(x))) → b(u(x))e(a(w(x))) → b(u(x))d(w(x)) → u(x)v(a(w(x))) → b(u(x))v(b(w(x))) → b(u(x))b(c(x)) → e(b(x))b(d(x)) → v(b(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)))) |
∞ |
11.18
Statisticsiterations: 10 equalities (active): 157 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 10.774 time/normalization: 0.036 time/overlaps: 0.068 time/orientation constraints: 4.41 time/project: 0 time/sat: 4.632 time/update context: 0.049 Convergent TRS(VAR x)
Completion of SK90_3.29
(RULES c(w(x)) → u(x)a(u(x)) → v(b(w(x)))a(d(x)) → v(a(x))a(c(x)) → e(a(x))e(b(w(x))) → v(b(w(x)))e(a(w(x))) → v(b(w(x)))v(a(w(x))) → v(b(w(x)))d(w(x)) → u(x)b(u(x)) → v(b(w(x)))b(c(x)) → e(b(x))b(d(x)) → v(b(x))) |
0.16
Statisticsiterations: 5 equalities (active): 54 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.132 time/normalization: 0.006 time/overlaps: 0.014 time/orientation constraints: 0.013 time/project: 0 time/sat: 0.006 time/update context: 0.005 Convergent TRS(VAR x)
Completion of SK90_3.29
(RULES d(w(x)) → u(x)c(w(x)) → u(x)a(u(x)) → b(u(x))a(d(x)) → v(a(x))a(c(x)) → e(a(x))e(a(w(x))) → b(u(x))v(a(w(x))) → b(u(x))v(b(w(x))) → b(u(x))e(b(w(x))) → b(u(x))b(c(x)) → e(b(x))b(d(x)) → v(b(x))) |
SK90_3.30 |
0.01
Statisticsiterations: 3 equalities (active): 12 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 time/project: 0 time/sat: 0 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) |
0.05
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) |
0.07
Statisticsiterations: 3 equalities (active): 13 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: 0.041 time/project: 0 time/sat: 0.006 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) |
0.09
Statisticsiterations: 3 equalities (active): 13 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.078 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.057 time/project: 0 time/sat: 0.011 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) |
0.02
Statisticsiterations: 3 equalities (active): 13 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: 0.001 time/project: 0 time/sat: 0 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 |
0.00
Statisticsiterations: 1 equalities (active): 3 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 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))) |
0.02
Statisticsiterations: 1 equalities (active): 3 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: 0.008 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: 0.009 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 SK90_3.31
(RULES i(x) → g(f(x,x))f(x,h(y)) → j(x)f(h(x),y) → j(h(x))) |
0.00
Statisticsiterations: 1 equalities (active): 3 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 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 |
0.00
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 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,) |
0.01
Statisticsiterations: 2 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: 0.002 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: 0.005 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 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 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 |
0.00
Statisticsiterations: 2 equalities (active): 5 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 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,) |
0.02
Statisticsiterations: 2 equalities (active): 5 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: 0.009 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,) |
0.02
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: 0.009 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: 0.001 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 SK90_3.33
(RULES g(a) → af(x) → x,g(g(x)) → x,) |
TPDB_secret2006_torpa_secr10 |
0.50
Statisticsiterations: 7 equalities (active): 113 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 0.386 time/normalization: 0.056 time/overlaps: 0.033 time/orientation constraints: 0.026 time/project: 0 time/sat: 0.001 time/update context: 0.01 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr10
(RULES a(b(c(b(x)))) → c(c(b(x)))b(c(b(a(x)))) → b(c(c(x)))a(a(x)) → c(b(a(x)))a(b(c(c(x)))) → c(c(x))b(c(a(c(x)))) → b(c(c(c(x))))c(b(c(c(x)))) → c(c(c(x)))c(b(c(b(x)))) → c(c(c(b(x))))c(c(a(x))) → c(c(c(x)))a(c(b(x))) → c(c(c(b(x))))a(c(c(x))) → c(c(c(x)))a(c(a(x))) → c(c(c(x)))c(c(c(c(x)))) → c(c(c(x)))c(c(b(a(x)))) → c(c(x))b(c(c(b(x)))) → b(c(b(x)))c(b(a(c(x)))) → c(a(c(x)))b(a(b(x))) → b(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)))) |
13.69
Statisticsiterations: 7 equalities (active): 127 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.008 time/maxk: 13.314 time/normalization: 0.174 time/overlaps: 0.069 time/orientation constraints: 1.477 time/project: 0 time/sat: 5.695 time/update context: 0.149 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr10
(RULES a(a(c(x))) → c(a(c(x)))a(a(a(x))) → c(c(c(x)))c(b(c(c(x)))) → c(c(c(x)))a(b(c(b(x)))) → c(c(b(x)))a(a(b(x))) → c(b(x))a(c(c(x))) → c(c(c(x)))b(a(a(x))) → b(c(c(x)))c(a(a(x))) → c(c(x))b(c(a(c(x)))) → b(c(c(c(x))))a(b(c(c(x)))) → c(c(x))a(c(b(x))) → c(c(c(b(x))))c(c(a(x))) → c(c(c(x)))a(c(a(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(c(b(x)))) → c(c(c(b(x))))c(b(a(x))) → a(a(x))b(a(b(x))) → b(x)) |
9.64
Statisticsiterations: 6 equalities (active): 114 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 9.36 time/normalization: 0.11 time/overlaps: 0.039 time/orientation constraints: 1.62 time/project: 0 time/sat: 4.973 time/update context: 0.074 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr10
(RULES a(b(c(b(x)))) → c(c(b(x)))b(c(b(a(x)))) → b(c(c(x)))a(a(x)) → c(b(a(x)))b(c(a(c(x)))) → b(c(c(c(x))))a(b(c(c(x)))) → c(c(x))a(c(b(x))) → c(c(c(b(x))))a(c(c(x))) → c(c(c(x)))c(c(a(x))) → c(c(c(x)))c(b(c(c(x)))) → c(c(c(x)))c(b(c(b(x)))) → c(c(c(b(x))))a(c(a(x))) → c(c(c(x)))c(c(c(c(x)))) → c(c(c(x)))b(c(c(b(x)))) → b(c(b(x)))c(c(b(a(x)))) → c(c(x))c(b(a(c(x)))) → c(a(c(x)))b(a(b(x))) → b(x)) |
5.68
Statisticsiterations: 9 equalities (active): 116 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 5.438 time/normalization: 0.147 time/overlaps: 0.048 time/orientation constraints: 0.031 time/project: 0 time/sat: 0.088 time/update context: 0.104 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr10
(RULES a(a(a(c(x)))) → a(a(a(x)))b(a(a(c(x)))) → b(a(a(a(x))))a(a(a(a(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)))c(c(x)) → a(b(a(a(x))))a(a(b(a(x)))) → a(a(x))c(a(a(x))) → a(b(a(a(x))))c(b(x)) → a(a(b(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 |
0.33
Statisticsiterations: 6 equalities (active): 100 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.286 time/normalization: 0.02 time/overlaps: 0.008 time/orientation constraints: 0.028 time/project: 0 time/sat: 0.002 time/update context: 0.008 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr4
(RULES d(c(c(x))) → c(c(c(x)))d(b(x)) → c(c(x))b(b(x)) → c(c(c(x)))b(d(x)) → c(c(x))a(x) → c(c(c(x)))c(d(x)) → c(c(c(x)))c(b(x)) → c(c(c(x)))b(c(c(x))) → c(c(c(x)))e(b(x)) → c(c(c(e(x))))e(d(x)) → c(c(c(e(x))))c(c(c(c(x)))) → c(c(c(x)))e(c(x)) → c(c(c(e(x))))d(d(x)) → b(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)))) |
81.69
Statisticsiterations: 17 equalities (active): 303 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.027 time/maxk: 80.657 time/normalization: 0.499 time/overlaps: 0.195 time/orientation constraints: 6.621 time/project: 0 time/sat: 24.239 time/update context: 1 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr4
(RULES b(x) → d(d(x))d(d(d(c(x)))) → a(x)d(d(d(d(x)))) → a(x)a(c(x)) → a(x)e(a(x)) → e(d(x))a(e(x)) → e(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))a(a(x)) → a(x)d(a(x)) → a(x)c(a(x)) → a(x)e(c(x)) → e(d(x))a(d(x)) → a(x)c(c(x)) → d(d(d(x)))c(d(x)) → a(x)) |
19.95
Statisticsiterations: 10 equalities (active): 219 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.01 time/maxk: 19.454 time/normalization: 0.145 time/overlaps: 0.117 time/orientation constraints: 4.698 time/project: 0 time/sat: 3.545 time/update context: 0.222 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr4
(RULES c(b(x)) → b(b(x))b(b(c(x))) → b(b(x))b(b(e(x))) → e(d(x))c(e(d(x))) → e(d(x))d(e(d(x))) → e(d(x))b(e(d(x))) → e(d(x))a(x) → b(b(x))e(e(d(x))) → e(d(e(x)))e(d(c(x))) → e(d(x))e(b(x)) → e(d(x))e(c(x)) → e(d(x))c(d(x)) → b(b(x))b(b(b(x))) → b(b(x))b(b(d(x))) → b(b(x))b(d(c(x))) → b(b(x))d(b(x)) → b(d(x))c(c(x)) → b(d(x))d(d(x)) → b(x)) |
1.40
Statisticsiterations: 6 equalities (active): 98 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 1.334 time/normalization: 0.035 time/overlaps: 0.011 time/orientation constraints: 0.024 time/project: 0 time/sat: 0.022 time/update context: 0.04 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr4
(RULES b(x) → d(d(x))d(d(d(x))) → c(c(x))a(d(x)) → a(x)d(c(c(x))) → a(x)e(a(x)) → a(e(x))e(d(x)) → a(e(x))e(c(x)) → a(e(x))d(a(x)) → a(x)a(c(x)) → a(x)a(a(x)) → a(x)c(c(c(x))) → a(x)c(a(x)) → a(x)c(d(x)) → a(x)) |
TPDB_thiemann27 | ∞ | ∞ | ∞ | ∞ | ∞ |
TPDB_zantema_z115 |
0.40
Statisticsiterations: 6 equalities (active): 95 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.318 time/normalization: 0.04 time/overlaps: 0.021 time/orientation constraints: 0.038 time/project: 0 time/sat: 0.004 time/update context: 0.008 Convergent TRS(VAR x)
Completion of TPDB_zantema_z115
(RULES c(d(x)) → a(a(x))d(a(a(x))) → c(c(c(x)))c(c(c(a(x)))) → c(c(c(x)))a(c(a(a(x)))) → c(c(c(x)))c(c(a(a(x)))) → c(c(c(x)))a(a(a(a(x)))) → c(c(c(x)))c(c(c(c(x)))) → c(c(c(x)))a(a(d(x))) → c(c(c(x)))d(c(x)) → a(a(x))a(c(c(x))) → c(c(c(x)))d(d(x)) → c(c(a(c(x))))a(a(c(x))) → c(a(a(x)))b(x) → c(c(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))) |
33.99
Statisticsiterations: 13 equalities (active): 237 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.017 time/maxk: 33.128 time/normalization: 0.378 time/overlaps: 0.224 time/orientation constraints: 3.463 time/project: 0 time/sat: 3.32 time/update context: 0.551 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(b(x))) → a(b(x))c(a(a(x))) → b(d(x))c(b(x)) → a(b(x))d(b(x)) → b(d(x))a(a(b(x))) → a(b(x))a(a(c(x))) → b(d(x))d(a(b(x))) → a(b(x))a(a(d(x))) → a(b(x))a(d(d(x))) → a(b(x))a(a(a(a(x)))) → a(b(x))b(d(a(c(x)))) → a(b(x))b(d(a(d(x)))) → a(b(x))b(d(d(x))) → a(b(x))d(a(a(x))) → a(b(x))d(d(d(x))) → a(b(x))a(b(a(x))) → a(b(x))b(a(a(x))) → a(b(x))a(b(d(x))) → a(b(x))b(c(x)) → a(b(x))b(a(b(x))) → a(b(x))b(b(x)) → a(b(x))b(a(c(x))) → d(d(x))) |
33.86
Statisticsiterations: 11 equalities (active): 247 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.015 time/maxk: 33.296 time/normalization: 0.231 time/overlaps: 0.047 time/orientation constraints: 5.355 time/project: 0 time/sat: 13.507 time/update context: 0.326 Convergent TRS(VAR x)
Completion of TPDB_zantema_z115
(RULES d(d(x)) → b(a(c(x)))c(d(x)) → a(a(x))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))b(a(a(x))) → b(b(x))a(a(d(x))) → b(b(x))d(b(x)) → b(d(x))b(c(x)) → b(b(x))a(a(c(x))) → b(d(x))d(a(a(x))) → b(b(x))b(d(a(d(x)))) → b(b(x))b(d(a(c(x)))) → b(b(x))a(a(a(a(x)))) → b(b(x))b(b(a(x))) → b(b(x))b(b(d(x))) → b(b(x))b(b(b(x))) → b(b(x))) |
1.28
Statisticsiterations: 6 equalities (active): 119 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 1.165 time/normalization: 0.055 time/overlaps: 0.021 time/orientation constraints: 0.029 time/project: 0 time/sat: 0.017 time/update context: 0.046 Convergent TRS(VAR x)
Completion of TPDB_zantema_z115
(RULES c(d(x)) → a(a(x))d(c(x)) → a(a(x))d(a(a(x))) → c(c(c(x)))c(c(c(a(x)))) → c(c(c(x)))a(a(a(a(x)))) → c(c(c(x)))a(c(a(a(x)))) → c(c(c(x)))c(c(a(a(x)))) → c(c(c(x)))a(a(d(x))) → c(c(c(x)))d(d(x)) → c(c(a(c(x))))c(c(c(c(x)))) → c(c(c(x)))a(c(c(x))) → c(c(c(x)))a(a(c(x))) → c(a(a(x)))b(x) → c(c(x))) |
TPTP_BOO027-1_theory |
0.01
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.001 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0 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))) |
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: 0.002 time/orientation constraints: 0.009 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))) |
0.03
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.024 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.013 time/project: 0 time/sat: 0.004 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))) |
0.01
Statisticsiterations: 2 equalities (active): 8 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0 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))) |
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 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0 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))) |
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: 0.008 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.007 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 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0 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 |
0.00
Statisticsiterations: 1 equalities (active): 3 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 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))) |
0.03
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.021 time/normalization: 0 time/overlaps: 0.002 time/orientation constraints: 0.013 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))) |
0.03
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.018 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.005 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: 0.002 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0 time/project: 0 time/sat: 0 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 | ∞ |
0.03
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)) |
0.03
Statisticsiterations: 1 equalities (active): 2 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.025 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.021 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)) |
0.03
Statisticsiterations: 2 equalities (active): 2 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0 time/maxk: 0.012 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.01 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)) |
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 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: 0.003 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) |
0.01
Statisticsiterations: 1 equalities (active): 1 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 )
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: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.002 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR )
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: 0.001 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) |
TPTP_GRP010-4_theory |
0.24
Statisticsiterations: 7 equalities (active): 77 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 0.087 time/normalization: 0.072 time/overlaps: 0.038 time/orientation constraints: 0.007 time/project: 0 time/sat: 0.001 time/update context: 0.004 Convergent TRS(VAR x y z)
Completion of TPTP_GRP010-4_theory
(RULES multiply(inverse(x),x) → identitymultiply(c,b) → identitymultiply(x,inverse(x)) → identitymultiply(b,c) → identityinverse(b) → cinverse(c) → binverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(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,) |
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,) |
6.98
Statisticsiterations: 9 equalities (active): 120 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.008 time/maxk: 6.582 time/normalization: 0.184 time/overlaps: 0.104 time/orientation constraints: 0.652 time/project: 0 time/sat: 1.109 time/update context: 0.15 Convergent TRS(VAR x y z)
Completion of TPTP_GRP010-4_theory
(RULES multiply(inverse(x),x) → identitymultiply(x,inverse(x)) → identityc → inverse(b)inverse(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,) |
7.45
Statisticsiterations: 9 equalities (active): 134 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 7.109 time/normalization: 0.144 time/overlaps: 0.066 time/orientation constraints: 0.909 time/project: 0 time/sat: 1.808 time/update context: 0.126 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,) |
0.92
Statisticsiterations: 8 equalities (active): 80 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 0.738 time/normalization: 0.066 time/overlaps: 0.054 time/orientation constraints: 0.013 time/project: 0 time/sat: 0.04 time/update context: 0.037 Convergent TRS(VAR x y z)
Completion of TPTP_GRP010-4_theory
(RULES multiply(inverse(x),x) → multiply(c,b)multiply(inverse(x),multiply(x,y)) → y,inverse(b) → cinverse(c) → bmultiply(x,inverse(x)) → multiply(c,b)inverse(multiply(x,y)) → multiply(inverse(y),inverse(x))inverse(inverse(x)) → x,multiply(x,multiply(c,b)) → x,multiply(b,c) → multiply(c,b)multiply(b,multiply(c,x)) → x,multiply(x,multiply(inverse(x),y)) → y,multiply(c,multiply(b,x)) → x,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))identity → multiply(c,b)) |
TPTP_GRP011-4_theory |
0.31
Statisticsiterations: 8 equalities (active): 90 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 0.138 time/normalization: 0.058 time/overlaps: 0.07 time/orientation constraints: 0.009 time/project: 0 time/sat: 0.001 time/update context: 0.007 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,) |
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,) |
3.18
Statisticsiterations: 7 equalities (active): 93 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 2.843 time/normalization: 0.158 time/overlaps: 0.09 time/orientation constraints: 0.31 time/project: 0 time/sat: 0.508 time/update context: 0.058 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,) |
2.86
Statisticsiterations: 7 equalities (active): 93 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 2.603 time/normalization: 0.084 time/overlaps: 0.078 time/orientation constraints: 0.442 time/project: 0 time/sat: 0.773 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)) → 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,) |
0.68
Statisticsiterations: 7 equalities (active): 69 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 0.516 time/normalization: 0.051 time/overlaps: 0.061 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.029 time/update context: 0.017 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,) |
TPTP_GRP012-4_theory |
0.04
Statisticsiterations: 4 equalities (active): 28 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.009 time/normalization: 0.007 time/overlaps: 0.022 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 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))) |
0.46
Statisticsiterations: 4 equalities (active): 47 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.338 time/normalization: 0.046 time/overlaps: 0.051 time/orientation constraints: 0.086 time/project: 0 time/sat: 0.037 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))) |
0.36
Statisticsiterations: 4 equalities (active): 47 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.301 time/normalization: 0.016 time/overlaps: 0.021 time/orientation constraints: 0.111 time/project: 0 time/sat: 0.048 time/update context: 0.004 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))) |
0.09
Statisticsiterations: 4 equalities (active): 28 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.057 time/normalization: 0.007 time/overlaps: 0.013 time/orientation constraints: 0.001 time/project: 0 time/sat: 0.001 time/update context: 0.003 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 |
0.00
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 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))) |
0.00
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: 0.003 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_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 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0 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 |
0.09
Statisticsiterations: 6 equalities (active): 44 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.031 time/normalization: 0.019 time/overlaps: 0.02 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0.002 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))) |
1.12
Statisticsiterations: 6 equalities (active): 63 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 0.974 time/normalization: 0.056 time/overlaps: 0.05 time/orientation constraints: 0.144 time/project: 0 time/sat: 0.063 time/update context: 0.026 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))) |
0.88
Statisticsiterations: 6 equalities (active): 63 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.772 time/normalization: 0.04 time/overlaps: 0.037 time/orientation constraints: 0.173 time/project: 0 time/sat: 0.098 time/update context: 0.015 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))) |
0.31
Statisticsiterations: 6 equalities (active): 44 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.194 time/normalization: 0.031 time/overlaps: 0.052 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.007 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))) |
TPTP_GRP454-1_theory |
0.83
Statisticsiterations: 14 equalities (active): 133 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.011 time/maxk: 0.501 time/normalization: 0.13 time/overlaps: 0.103 time/orientation constraints: 0.017 time/project: 0 time/sat: 0.003 time/update context: 0.022 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,inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(b,multiply(inverse(b),a)) → a,inverse(inverse(b)) → b,multiply(b,identity) → b,multiply(identity,b) → b,multiply(b,inverse(b)) → identitymultiply(inverse(b),b) → identityinverse(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,) |
46.29
Statisticsiterations: 11 equalities (active): 172 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.031 time/maxk: 45.26 time/normalization: 0.37 time/overlaps: 0.392 time/orientation constraints: 1.071 time/project: 0 time/sat: 33.318 time/update context: 0.348 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(inverse(b),multiply(b,a)) → a,multiply(b,identity) → b,multiply(b,inverse(b)) → identitymultiply(identity,b) → b,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
32.97
Statisticsiterations: 11 equalities (active): 183 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.028 time/maxk: 32.128 time/normalization: 0.377 time/overlaps: 0.232 time/orientation constraints: 1.4 time/project: 0 time/sat: 22.958 time/update context: 0.254 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,identity) → b,multiply(b,inverse(b)) → identitymultiply(identity,b) → b,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
7.41
Statisticsiterations: 13 equalities (active): 145 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.011 time/maxk: 6.989 time/normalization: 0.167 time/overlaps: 0.091 time/orientation constraints: 0.433 time/project: 0 time/sat: 2.873 time/update context: 0.127 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,identity) → b,multiply(b,inverse(b)) → identitymultiply(identity,b) → b,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
TPTP_GRP457-1_theory |
0.97
Statisticsiterations: 14 equalities (active): 133 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.014 time/maxk: 0.599 time/normalization: 0.147 time/overlaps: 0.113 time/orientation constraints: 0.022 time/project: 0 time/sat: 0.003 time/update context: 0.026 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,inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(b,multiply(inverse(b),a)) → a,inverse(inverse(b)) → b,multiply(b,identity) → b,multiply(identity,b) → b,multiply(b,inverse(b)) → identitymultiply(inverse(b),b) → identityinverse(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,) |
293.93
Statisticsiterations: 21 equalities (active): 360 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.092 time/maxk: 289.686 time/normalization: 2.342 time/overlaps: 1.076 time/orientation constraints: 4.784 time/project: 0 time/sat: 150.299 time/update context: 2.534 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(b,multiply(inverse(b),a)) → a,multiply(inverse(b),multiply(b,a)) → a,multiply(identity,b) → b,multiply(b,identity) → b,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
89.90
Statisticsiterations: 15 equalities (active): 256 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.029 time/maxk: 88.605 time/normalization: 0.432 time/overlaps: 0.387 time/orientation constraints: 4.337 time/project: 0 time/sat: 57.878 time/update context: 0.568 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,multiply(inverse(b),a)) → a,multiply(b,identity) → b,multiply(identity,b) → b,multiply(b,inverse(b)) → identitymultiply(inverse(b),multiply(b,a)) → a,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
15.59
Statisticsiterations: 15 equalities (active): 190 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.016 time/maxk: 15.068 time/normalization: 0.195 time/overlaps: 0.174 time/orientation constraints: 0.585 time/project: 0 time/sat: 4.762 time/update context: 0.316 Convergent TRS(VAR b a c)
Completion of TPTP_GRP457-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))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(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))multiply(b,identity) → b,multiply(identity,b) → b,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
TPTP_GRP460-1_theory |
1.11
Statisticsiterations: 16 equalities (active): 125 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.018 time/maxk: 0.525 time/normalization: 0.235 time/overlaps: 0.152 time/orientation constraints: 0.02 time/project: 0 time/sat: 0.004 time/update context: 0.023 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(identity,b) → b,multiply(b,inverse(b)) → identitymultiply(inverse(b),multiply(b,a)) → a,inverse(inverse(b)) → b,multiply(b,identity) → b,multiply(inverse(b),b) → identitymultiply(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,) |
223.23
Statisticsiterations: 23 equalities (active): 323 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.077 time/maxk: 220.528 time/normalization: 1.375 time/overlaps: 0.583 time/orientation constraints: 3.854 time/project: 0 time/sat: 139.229 time/update context: 1.563 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(b,multiply(inverse(b),a)) → a,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
134.84
Statisticsiterations: 18 equalities (active): 255 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.052 time/maxk: 133.519 time/normalization: 0.566 time/overlaps: 0.366 time/orientation constraints: 3.378 time/project: 0 time/sat: 94.699 time/update context: 0.92 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(b,multiply(inverse(b),a)) → a,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
120.03
Statisticsiterations: 25 equalities (active): 279 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.041 time/maxk: 117.944 time/normalization: 0.761 time/overlaps: 0.629 time/orientation constraints: 1.93 time/project: 0 time/sat: 70.659 time/update context: 0.915 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(b,multiply(inverse(b),a)) → a,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
TPTP_GRP463-1_theory |
1.15
Statisticsiterations: 16 equalities (active): 125 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.021 time/maxk: 0.538 time/normalization: 0.255 time/overlaps: 0.146 time/orientation constraints: 0.022 time/project: 0 time/sat: 0.003 time/update context: 0.027 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,inverse(inverse(b)) → b,multiply(b,identity) → b,multiply(inverse(b),b) → identitymultiply(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,) |
∞ |
87.62
Statisticsiterations: 16 equalities (active): 263 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.037 time/maxk: 84.916 time/normalization: 1.371 time/overlaps: 0.635 time/orientation constraints: 4.371 time/project: 0 time/sat: 40.999 time/update context: 0.871 Convergent TRS(VAR b a c)
Completion of TPTP_GRP463-1_theory
(RULES divide(b,a) → multiply(b,inverse(a))inverse(multiply(b,a)) → multiply(inverse(a),inverse(b))multiply(multiply(b,a),c,lass="var">c) → multiply(b,multiply(a,c,lass="var">c))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,) |
42.91
Statisticsiterations: 19 equalities (active): 238 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.022 time/maxk: 41.946 time/normalization: 0.318 time/overlaps: 0.359 time/orientation constraints: 0.895 time/project: 0 time/sat: 25.203 time/update context: 0.454 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 |
2.12
Statisticsiterations: 13 equalities (active): 187 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.028 time/maxk: 1.508 time/normalization: 0.269 time/overlaps: 0.126 time/orientation constraints: 0.033 time/project: 0 time/sat: 0.003 time/update context: 0.06 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))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(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)) → identitymultiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,inverse(inverse(c,lass="var">c)) → c,inverse(identity) → identity) |
∞ | ∞ | ∞ |
12.29
Statisticsiterations: 13 equalities (active): 188 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.027 time/maxk: 11.475 time/normalization: 0.388 time/overlaps: 0.247 time/orientation constraints: 0.025 time/project: 0 time/sat: 0.473 time/update context: 0.414 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))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(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)) → identitymultiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,inverse(identity) → identityinverse(inverse(c,lass="var">c)) → c,) |
TPTP_GRP484-1_theory | ∞ |
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,) |
159.58
Statisticsiterations: 16 equalities (active): 251 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.048 time/maxk: 157.401 time/normalization: 1.047 time/overlaps: 0.53 time/orientation constraints: 4.319 time/project: 0 time/sat: 100.205 time/update context: 1.175 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,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),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) → identitymultiply(c,lass="var">c,inverse(c,lass="var">c)) → identityinverse(identity) → identityinverse(inverse(c,lass="var">c)) → c,) |
230.09
Statisticsiterations: 20 equalities (active): 280 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.081 time/maxk: 227.648 time/normalization: 1.087 time/overlaps: 0.645 time/orientation constraints: 8.471 time/project: 0 time/sat: 119.353 time/update context: 2.194 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(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,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),c,lass="var">c) → identityinverse(identity) → identitymultiply(c,lass="var">c,identity) → c,multiply(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(identity,c,lass="var">c) → c,inverse(inverse(c,lass="var">c)) → c,) |
131.82
Statisticsiterations: 25 equalities (active): 314 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.056 time/maxk: 130.254 time/normalization: 0.595 time/overlaps: 0.379 time/orientation constraints: 2.551 time/project: 0 time/sat: 63.597 time/update context: 1.288 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(inverse(c,lass="var">c),c,lass="var">c) → identityinverse(identity) → identitymultiply(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(c,lass="var">c,identity) → c,multiply(identity,c,lass="var">c) → c,inverse(inverse(c,lass="var">c)) → c,) |
TPTP_GRP487-1_theory | ∞ |
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) |
472.55
Statisticsiterations: 27 equalities (active): 384 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.177 time/maxk: 468.597 time/normalization: 2.284 time/overlaps: 0.567 time/orientation constraints: 7.577 time/project: 0 time/sat: 213.63 time/update context: 4.335 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)) → identitymultiply(inverse(c,lass="var">c),c,lass="var">c) → identityinverse(identity) → identityinverse(inverse(c,lass="var">c)) → c,) |
∞ |
25.58
Statisticsiterations: 17 equalities (active): 215 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.056 time/maxk: 24.332 time/normalization: 0.586 time/overlaps: 0.312 time/orientation constraints: 0.038 time/project: 0 time/sat: 0.604 time/update context: 0.595 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(identity,c,lass="var">c) → c,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)) → identityinverse(inverse(c,lass="var">c)) → c,multiply(inverse(c,lass="var">c),c,lass="var">c) → identityinverse(identity) → identity) |
TPTP_GRP490-1_theory |
3.10
Statisticsiterations: 14 equalities (active): 216 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.08 time/maxk: 2.127 time/normalization: 0.404 time/overlaps: 0.29 time/orientation constraints: 0.037 time/project: 0 time/sat: 0.003 time/update context: 0.077 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(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,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(identity,c,lass="var">c) → c,inverse(inverse(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) → 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,) |
∞ |
190.35
Statisticsiterations: 20 equalities (active): 315 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.073 time/maxk: 188.816 time/normalization: 0.572 time/overlaps: 0.483 time/orientation constraints: 4.896 time/project: 0 time/sat: 114.449 time/update context: 1.165 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(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,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(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,) |
20.30
Statisticsiterations: 15 equalities (active): 220 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.044 time/maxk: 19.463 time/normalization: 0.429 time/overlaps: 0.202 time/orientation constraints: 0.036 time/project: 0 time/sat: 0.397 time/update context: 0.451 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(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_GRP493-1_theory | ∞ |
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,) |
526.05
Statisticsiterations: 23 equalities (active): 336 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.33 time/maxk: 519.564 time/normalization: 3.701 time/overlaps: 1.038 time/orientation constraints: 4.201 time/project: 0 time/sat: 291.739 time/update context: 6.415 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) → identityinverse(inverse(b)) → b,multiply(inverse(b),multiply(b,a)) → a,inverse(identity) → identity) |
330.22
Statisticsiterations: 21 equalities (active): 300 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.161 time/maxk: 326.999 time/normalization: 1.448 time/overlaps: 0.72 time/orientation constraints: 6.311 time/project: 0 time/sat: 195.434 time/update context: 2.943 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(b,inverse(b)) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,multiply(inverse(b),multiply(b,a)) → a,multiply(identity,b) → b,inverse(identity) → identity) |
103.66
Statisticsiterations: 23 equalities (active): 262 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.076 time/maxk: 100.783 time/normalization: 1.07 time/overlaps: 0.721 time/orientation constraints: 1.585 time/project: 0 time/sat: 64.54 time/update context: 0.727 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(inverse(b),b) → identitymultiply(inverse(b),multiply(b,a)) → a,inverse(identity) → identitymultiply(b,inverse(b)) → identitymultiply(identity,b) → b,multiply(b,identity) → b,inverse(inverse(b)) → b,) |
TPTP_GRP496-1_theory | ∞ | ∞ |
179.34
Statisticsiterations: 19 equalities (active): 298 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.041 time/maxk: 176.494 time/normalization: 1.294 time/overlaps: 0.796 time/orientation constraints: 4.148 time/project: 0 time/sat: 113.671 time/update context: 0.892 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))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,multiply(inverse(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,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,) |
184.03
Statisticsiterations: 19 equalities (active): 287 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.038 time/maxk: 181.558 time/normalization: 0.984 time/overlaps: 0.733 time/orientation constraints: 7.123 time/project: 0 time/sat: 122.038 time/update context: 0.922 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))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(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,) |
86.91
Statisticsiterations: 38 equalities (active): 205 equalities (passive): 0 restarts: 2 time/cache: 0 time/set ops: 0.05 time/maxk: 83.1 time/normalization: 2.144 time/overlaps: 0.872 time/orientation constraints: 2.095 time/project: 0 time/sat: 49.274 time/update context: 0.665 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(identity,c,lass="var">c) → c,multiply(c,lass="var">c,identity) → c,multiply(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,inverse(inverse(c,lass="var">c)) → c,multiply(inverse(c,lass="var">c),c,lass="var">c) → identityinverse(identity) → identity) |
TPTP_HWC004-1_theory |
0.04
Statisticsiterations: 1 equalities (active): 10 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 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) |
0.01
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) |
0.01
Statisticsiterations: 1 equalities (active): 10 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 )
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) |
0.05
Statisticsiterations: 1 equalities (active): 10 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: 0.008 time/project: 0 time/sat: 0.003 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) |
0.00
Statisticsiterations: 1 equalities (active): 10 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_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 |
0.00
Statisticsiterations: 1 equalities (active): 6 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 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: 0.006 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 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: 0.007 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 TPTP_HWC004-2_theory
(RULES and(x,n0) → n0and(x,n1) → x,or(x,n0) → x,or(x,n1) → n1not(n0) → n1not(n1) → n0) |
0.00
Statisticsiterations: 1 equalities (active): 6 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 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 |
0.01
Statisticsiterations: 1 equalities (active): 3 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 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,) |
0.03
Statisticsiterations: 1 equalities (active): 3 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.023 time/normalization: 0 time/overlaps: 0.001 time/orientation constraints: 0.017 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: 0.015 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 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,) |
0.01
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: 0.001 time/orientation constraints: 0 time/project: 0 time/sat: 0 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 | ∞ |
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) |
5.70
Statisticsiterations: 6 equalities (active): 139 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 4.723 time/normalization: 0.287 time/overlaps: 0.377 time/orientation constraints: 1.601 time/project: 0 time/sat: 0.986 time/update context: 0.094 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(CongrAnd2(x),trans(AndTrue1,y)) → trans(AndTrue1,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(CongrOr1(x),trans(OrFalse2,y)) → trans(OrFalse2,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(CongrAnd1(x),CongrAnd2(y)) → trans(CongrAnd2(y),CongrAnd1(x))trans(CongrAnd1(x),CongrAnd1(y)) → CongrAnd1(trans(x,y))trans(CongrAnd2(x),CongrAnd2(y)) → CongrAnd2(trans(x,y))trans(CongrAnd1(x),trans(CongrAnd2(y),z)) → trans(CongrAnd2(y),trans(CongrAnd1(x),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(CongrOr2(x),CongrOr2(y)) → CongrOr2(trans(x,y))trans(CongrOr1(x),CongrOr1(y)) → CongrOr1(trans(x,y))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(CongrOr1(x),trans(CongrOr2(y),OrFalse2)) → trans(CongrOr2(y),trans(OrFalse2,x))trans(CongrOr1(x),trans(CongrOr2(y),OrTrue2)) → trans(CongrOr2(y),OrTrue2)trans(CongrAnd2(x),trans(CongrAnd1(y),AndTrue1)) → trans(CongrAnd1(y),trans(AndTrue1,x))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),AndFalse1)) → trans(CongrAnd1(y),AndFalse1)trans(CongrAnd2(x),trans(CongrAnd1(y),trans(AndFalse1,z))) → trans(CongrAnd1(y),trans(AndFalse1,z))trans(CongrAnd2(x),trans(CongrAnd1(y),trans(AndTrue1,z))) → trans(CongrAnd1(y),trans(AndTrue1,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) → reflCongrAnd1(refl) → reflCongrAnd2(refl) → reflCongrNot(refl) → refl) |
13.21
Statisticsiterations: 6 equalities (active): 127 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 12.295 time/normalization: 0.212 time/overlaps: 0.347 time/orientation constraints: 2.57 time/project: 0 time/sat: 7.818 time/update context: 0.089 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(CongrOr2(x),trans(OrFalse1,y)) → trans(OrFalse1,trans(x,y))trans(CongrOr1(x),trans(OrFalse2,y)) → trans(OrFalse2,trans(x,y))trans(CongrAnd2(x),trans(AndTrue1,y)) → trans(AndTrue1,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(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) |
3.61
Statisticsiterations: 7 equalities (active): 130 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.004 time/maxk: 2.998 time/normalization: 0.15 time/overlaps: 0.238 time/orientation constraints: 0.92 time/project: 0 time/sat: 0.794 time/update context: 0.063 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(CongrAnd1(x),CongrAnd1(y)) → CongrAnd1(trans(x,y))trans(CongrAnd2(x),CongrAnd2(y)) → CongrAnd2(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(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(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(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,CongrAnd1(y)),CongrAnd1(z)) → trans(x,CongrAnd1(trans(y,z)))trans(trans(x,CongrAnd2(y)),CongrAnd2(z)) → trans(x,CongrAnd2(trans(y,z)))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(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) |
aufgabe3_2 |
0.00
Statisticsiterations: 1 equalities (active): 2 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 x)
Completion of aufgabe3_2
(RULES f(f(x)) → g(x)f(g(x)) → g(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: 0.005 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 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: 0.008 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)
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: 0.001 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_2
(RULES f(f(x)) → g(x)f(g(x)) → g(f(x))) |
aufgabe3_3 |
0.00
Statisticsiterations: 3 equalities (active): 4 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 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,) |
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: 0.001 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: 0.005 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 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of aufgabe3_3
(RULES f(x) → x,) |
fggx |
0.00
Statisticsiterations: 2 equalities (active): 5 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 x)
Completion of fggx
(RULES g(g(g(x))) → x,f(x) → g(g(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,) |
0.03
Statisticsiterations: 2 equalities (active): 5 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.017 time/normalization: 0 time/overlaps: 0.006 time/orientation constraints: 0.009 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,) |
0.02
Statisticsiterations: 2 equalities (active): 5 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: 0.006 time/project: 0 time/sat: 0.006 time/update context: 0 Convergent TRS(VAR x)
Completion of fggx
(RULES g(g(g(x))) → x,f(x) → g(g(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 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x)
Completion of fggx
(RULES g(g(g(x))) → x,f(x) → g(g(x))) |
fib | ∞ |
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))) |
14.34
Statisticsiterations: 19 equalities (active): 130 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.009 time/maxk: 13.914 time/normalization: 0.109 time/overlaps: 0.108 time/orientation constraints: 5.369 time/project: 0 time/sat: 2.817 time/update context: 0.16 Convergent TRS(VAR x y)
Completion of fib
(RULES b(f(s(x)),f(x)) → g(x)b(s(0),0) → g(0)p(f(s(x)),f(x)) → u(g(x))p(x,s(y)) → s(p(x,y))f(s(s(x))) → u(g(x))b(u(g(x)),f(s(x))) → g(s(x))p(u(g(x)),f(s(x))) → u(g(s(x)))b(s(0),s(0)) → g(s(0))g(s(s(x))) → b(u(g(s(x))),u(g(x)))u(g(s(0))) → s(s(0))u(g(0)) → s(0)p(x,0) → x,f(0) → 0f(s(0)) → s(0)n(g(x)) → g(s(x))n(b(x,y)) → b(p(x,y),x)u(b(x,y)) → p(x,y)) |
41.63
Statisticsiterations: 15 equalities (active): 50 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.01 time/maxk: 41.223 time/normalization: 0.138 time/overlaps: 0.084 time/orientation constraints: 13.479 time/project: 0 time/sat: 20.277 time/update context: 0.173 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))) |
1.41
Statisticsiterations: 12 equalities (active): 43 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.002 time/maxk: 1.179 time/normalization: 0.062 time/overlaps: 0.079 time/orientation constraints: 0.22 time/project: 0 time/sat: 0.078 time/update context: 0.034 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))) |
lr_theory |
0.14
Statisticsiterations: 5 equalities (active): 55 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.042 time/normalization: 0.039 time/overlaps: 0.029 time/orientation constraints: 0.004 time/project: 0 time/sat: 0 time/update context: 0.002 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,) |
3.99
Statisticsiterations: 8 equalities (active): 96 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 3.558 time/normalization: 0.178 time/overlaps: 0.14 time/orientation constraints: 0.551 time/project: 0 time/sat: 0.164 time/update context: 0.075 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,) |
2.59
Statisticsiterations: 7 equalities (active): 88 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 2.259 time/normalization: 0.139 time/overlaps: 0.088 time/orientation constraints: 0.637 time/project: 0 time/sat: 0.252 time/update context: 0.04 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,) |
0.54
Statisticsiterations: 6 equalities (active): 59 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 0.374 time/normalization: 0.07 time/overlaps: 0.042 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.012 time/update context: 0.015 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 |
0.53
Statisticsiterations: 8 equalities (active): 88 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 0.165 time/normalization: 0.192 time/overlaps: 0.087 time/orientation constraints: 0.01 time/project: 0 time/sat: 0 time/update context: 0.007 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,) |
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,) |
9.01
Statisticsiterations: 11 equalities (active): 117 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 8.359 time/normalization: 0.29 time/overlaps: 0.193 time/orientation constraints: 1.059 time/project: 0 time/sat: 1.265 time/update context: 0.142 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,) |
1.52
Statisticsiterations: 7 equalities (active): 74 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 1.345 time/normalization: 0.061 time/overlaps: 0.04 time/orientation constraints: 0.541 time/project: 0 time/sat: 0.181 time/update context: 0.021 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,) |
1.39
Statisticsiterations: 8 equalities (active): 80 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 1.084 time/normalization: 0.162 time/overlaps: 0.077 time/orientation constraints: 0.009 time/project: 0 time/sat: 0.022 time/update context: 0.041 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,) |
slothrop_ackermann |
0.00
Statisticsiterations: 1 equalities (active): 3 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 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))) |
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))) |
0.02
Statisticsiterations: 1 equalities (active): 3 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: 0.008 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))) |
0.00
Statisticsiterations: 1 equalities (active): 3 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 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 | ∞ |
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,) |
18.49
Statisticsiterations: 7 equalities (active): 119 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.025 time/maxk: 17.561 time/normalization: 0.381 time/overlaps: 0.308 time/orientation constraints: 0.983 time/project: 0 time/sat: 10.905 time/update context: 0.179 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(f(x)) → f(symm(x))symm(g(x)) → g(symm(x))symm(trans(x,y)) → trans(symm(y),symm(x))g(refl) → reflsymm(refl) → reflsymm(symm(x)) → x,f(refl) → refltrans(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,) |
12.30
Statisticsiterations: 7 equalities (active): 115 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.017 time/maxk: 11.613 time/normalization: 0.246 time/overlaps: 0.183 time/orientation constraints: 1.356 time/project: 0 time/sat: 6.411 time/update context: 0.105 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(g(x),trans(g(y),z)) → trans(g(trans(x,y)),z)trans(f(x),trans(f(y),z)) → trans(f(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))f(refl) → reflsymm(refl) → reflsymm(symm(x)) → x,g(refl) → refltrans(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))) |
4.14
Statisticsiterations: 8 equalities (active): 93 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.01 time/maxk: 3.765 time/normalization: 0.165 time/overlaps: 0.104 time/orientation constraints: 0.398 time/project: 0 time/sat: 1.814 time/update context: 0.05 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(g(x),trans(g(y),z)) → trans(g(trans(x,y)),z)trans(f(x),trans(f(y),z)) → trans(f(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))) |
slothrop_cge3 | ∞ |
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,) |
18.53
Statisticsiterations: 8 equalities (active): 120 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.029 time/maxk: 17.624 time/normalization: 0.278 time/overlaps: 0.34 time/orientation constraints: 0.886 time/project: 0 time/sat: 13.143 time/update context: 0.109 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(h(y),z)) → trans(h(y),trans(g(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) → reflf(refl) → reflg(refl) → reflsymm(refl) → reflsymm(symm(x)) → x,trans(x,trans(symm(x),y)) → y,trans(x,refl) → x,trans(symm(x),trans(x,y)) → y,trans(g(x),trans(f(y),z)) → trans(f(y),trans(g(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(g(x),f(y)) → trans(f(y),g(x))trans(h(x),f(y)) → trans(f(y),h(x))) |
23.31
Statisticsiterations: 8 equalities (active): 118 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.029 time/maxk: 22.237 time/normalization: 0.435 time/overlaps: 0.276 time/orientation constraints: 1.75 time/project: 0 time/sat: 15.609 time/update context: 0.131 Convergent TRS(VAR x y z)
Completion of slothrop_cge3
(RULES 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(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))g(refl) → reflf(refl) → reflsymm(refl) → reflh(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(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(g(x),f(y)) → trans(f(y),g(x))trans(h(x),g(y)) → trans(g(y),h(x))trans(h(x),f(y)) → trans(f(y),h(x))) |
24.44
Statisticsiterations: 11 equalities (active): 134 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.02 time/maxk: 23.572 time/normalization: 0.275 time/overlaps: 0.331 time/orientation constraints: 0.742 time/project: 0 time/sat: 17.972 time/update context: 0.116 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(h(y),z)) → trans(h(y),trans(f(x),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(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))trans(x,trans(symm(x),y)) → y,symm(refl) → reflsymm(symm(x)) → x,h(refl) → reflf(refl) → reflg(refl) → refltrans(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(trans(x,y),z) → trans(x,trans(y,z))trans(refl,x) → x,trans(h(x),g(y)) → trans(g(y),h(x))) |
slothrop_endo |
0.60
Statisticsiterations: 7 equalities (active): 77 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.014 time/maxk: 0.165 time/normalization: 0.191 time/overlaps: 0.135 time/orientation constraints: 0.009 time/project: 0 time/sat: 0.001 time/update context: 0.007 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) → eh(i(x)) → i(h(x))i(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,h(e) → ei(e) → ei(i(x)) → x,f(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))) |
3.77
Statisticsiterations: 7 equalities (active): 92 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.013 time/maxk: 3.38 time/normalization: 0.16 time/overlaps: 0.109 time/orientation constraints: 0.508 time/project: 0 time/sat: 0.466 time/update context: 0.065 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))h(i(x)) → i(h(x))f(i(x),f(x,y)) → y,i(e) → ei(i(x)) → 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))) |
4.12
Statisticsiterations: 7 equalities (active): 94 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.008 time/maxk: 3.786 time/normalization: 0.123 time/overlaps: 0.107 time/orientation constraints: 0.873 time/project: 0 time/sat: 0.997 time/update context: 0.055 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))h(i(x)) → i(h(x))f(i(x),f(x,y)) → y,i(e) → ei(i(x)) → 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))) |
1.46
Statisticsiterations: 7 equalities (active): 76 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 1.147 time/normalization: 0.154 time/overlaps: 0.085 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.04 time/update context: 0.044 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) → eh(i(x)) → i(h(x))i(f(x,y)) → f(i(y),i(x))f(i(x),f(x,y)) → y,h(e) → ei(e) → ei(i(x)) → x,f(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 | ∞ |
3.14
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) |
3.11
Statisticsiterations: 5 equalities (active): 92 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 2.678 time/normalization: 0.125 time/overlaps: 0.099 time/orientation constraints: 1.096 time/project: 0 time/sat: 0.309 time/update context: 0.048 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(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) |
6.51
Statisticsiterations: 5 equalities (active): 97 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 5.972 time/normalization: 0.16 time/overlaps: 0.106 time/orientation constraints: 2.438 time/project: 0 time/sat: 1.899 time/update context: 0.068 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(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) |
1.49
Statisticsiterations: 6 equalities (active): 90 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.001 time/maxk: 1.317 time/normalization: 0.042 time/overlaps: 0.051 time/orientation constraints: 0.606 time/project: 0 time/sat: 0.173 time/update context: 0.019 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(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),ortrue1)) → trans(congror1(x2),ortrue1)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(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 | ∞ |
3.08
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) |
3.06
Statisticsiterations: 5 equalities (active): 92 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 2.667 time/normalization: 0.116 time/overlaps: 0.091 time/orientation constraints: 1.056 time/project: 0 time/sat: 0.316 time/update context: 0.054 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(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) |
5.06
Statisticsiterations: 5 equalities (active): 97 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 4.615 time/normalization: 0.12 time/overlaps: 0.083 time/orientation constraints: 1.869 time/project: 0 time/sat: 1.586 time/update context: 0.047 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(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) |
1.50
Statisticsiterations: 6 equalities (active): 90 equalities (passive): 0 restarts: 1 time/cache: 0 time/set ops: 0.001 time/maxk: 1.321 time/normalization: 0.043 time/overlaps: 0.053 time/orientation constraints: 0.585 time/project: 0 time/sat: 0.18 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(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(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),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(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 |
0.01
Statisticsiterations: 3 equalities (active): 7 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 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: 0.01 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) |
0.02
Statisticsiterations: 3 equalities (active): 7 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: 0.009 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) |
0.04
Statisticsiterations: 3 equalities (active): 7 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.029 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.016 time/project: 0 time/sat: 0.007 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 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 |
0.22
Statisticsiterations: 7 equalities (active): 63 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.078 time/normalization: 0.052 time/overlaps: 0.059 time/orientation constraints: 0.004 time/project: 0 time/sat: 0 time/update context: 0.005 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))f(i(x),f(x,y)) → y,i(e) → ei(i(x)) → x,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,) |
0.78
Statisticsiterations: 6 equalities (active): 55 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 0.645 time/normalization: 0.054 time/overlaps: 0.046 time/orientation constraints: 0.162 time/project: 0 time/sat: 0.034 time/update context: 0.015 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,) |
0.77
Statisticsiterations: 6 equalities (active): 60 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.678 time/normalization: 0.031 time/overlaps: 0.036 time/orientation constraints: 0.212 time/project: 0 time/sat: 0.099 time/update context: 0.01 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,) |
0.76
Statisticsiterations: 7 equalities (active): 63 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0.002 time/maxk: 0.596 time/normalization: 0.077 time/overlaps: 0.05 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.019 time/update context: 0.018 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))f(i(x),f(x,y)) → y,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 |
0.02
Statisticsiterations: 4 equalities (active): 17 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 time/normalization: 0.002 time/overlaps: 0.004 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y z)
Completion of slothrop_groups_conj
(RULES f(x,i(x)) → ef(i(x),x) → ef(i(x),f(x,y)) → y,i(i(x)) → x,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))) |
0.54
Statisticsiterations: 4 equalities (active): 59 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.444 time/normalization: 0.028 time/overlaps: 0.041 time/orientation constraints: 0.148 time/project: 0 time/sat: 0.053 time/update context: 0.01 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))) |
0.51
Statisticsiterations: 4 equalities (active): 59 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.445 time/normalization: 0.013 time/overlaps: 0.021 time/orientation constraints: 0.206 time/project: 0 time/sat: 0.072 time/update context: 0.006 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))) |
0.03
Statisticsiterations: 4 equalities (active): 17 equalities (passive): 0 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.017 time/normalization: 0.003 time/overlaps: 0.002 time/orientation constraints: 0.001 time/project: 0 time/sat: 0 time/update context: 0.001 Convergent TRS(VAR x y z)
Completion of slothrop_groups_conj
(RULES f(x,i(x)) → ef(i(x),x) → ef(i(x),f(x,y)) → y,i(i(x)) → x,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 |
0.00
Statisticsiterations: 1 equalities (active): 2 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 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,) |
0.01
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 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: 0.008 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.007 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,) |
0.00
Statisticsiterations: 1 equalities (active): 2 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 x y)
Completion of slothrop_hard
(RULES plus(x,s(y)) → s(plus(x,y))plus(x,z) → x,) |
successes | 81 | 89 | 86 | 89 | 97 |
avg. time | 2.150 | 33.552 | 37.320 | 41.021 | 11.587 |