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
MaxcompDP | Maxcomp | mkbTT | KBCV | |
AD93_Z22 | ∞ | ⊥ | ⊥ | 29.52 |
ASK93_1 |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 4 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
OutputEQUATIONS:
Completion of ASK93_1
w(a(x)) = a(b(x)) a(c(x)) = a(b(c(x))) COMPLETE TRS: RULES: a(b(x)) -> w(a(x)) w(a(c(x))) -> a(c(x)) SUCCESS Search time: 0.02 seconds |
0.02
OutputCOMPLETE SYSTEM: a(b(x)) -> w(a(x)) w(a(c(x))) -> a(c(x)) STATISTICS: General number of iterations: 4 number of nodes: 7 number of processes: 2 time for orient: 0.01 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.000185 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 5 (yes: 5, timeouts: 0) time limit for check: 2.00 termination time: 0.01 Deduction critical pair criterion: all redundant CPs in total: 2 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.002692 Two: 0.000000 COMPLETE SYSTEM: a(b(x)) -> w(a(x)) w(a(c(x))) -> a(c(x)) |
0.69 |
ASK93_2 | ∞ | ∞ | ⊥ | ∞ |
ASK93_5 | ∞ | ⊥ | ⊥ | ∞ |
ASK93_6 |
0.25
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 3 equalities: 37 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.171 time/normalization: 0.008 time/overlaps: 0.038 time/orientation constraints: 0.026 time/project: 0 time/sat: 0.036 time/update context: 0.008 Convergent TRS(VAR z)
Completion of ASK93_6
(RULES i(y(z)) → a(z)x(w(a(z))) → u(z)x(w(e(g(z)))) → x(w(e(f(z))))x(w(e(f(c(z))))) → o(z)x(w(d(y(z)))) → u(z)x(w(d(g(z)))) → u(b(z))w(e(f(j(z)))) → w(e(z))i(g(c(z))) → e(f(c(z)))h(z) → w(e(f(z)))a(b(z)) → i(g(z))d(g(c(z))) → e(g(c(z)))x(w(i(z))) → x(w(d(z)))u(b(c(z))) → o(z)j(f(z)) → z,y(b(z)) → g(z)) |
0.28
OutputEQUATIONS:
Completion of ASK93_6
x(w(e(f(z)))) = x(w(e(g(z)))) e(g(c(z))) = d(g(c(z))) x(w(d(z))) = x(w(i(z))) u(b(c(z))) = o(z) x(w(i(g(c(z))))) = o(z) x(w(a(z))) = u(z) a(b(c(z))) = e(f(c(z))) j(f(z)) = z h(j(z)) = w(e(z)) y(b(z)) = g(z) i(y(z)) = a(z) COMPLETE TRS: RULES: j(f(z)) -> z u(z) -> x(w(d(y(z)))) e(f(c(z))) -> i(y(b(c(z)))) w(i(y(b(c(x))))) -> h(c(x)) x(w(i(z))) -> x(w(d(z))) o(z) -> x(h(c(z))) w(e(z)) -> h(j(z)) g(z) -> y(b(z)) a(z) -> i(y(z)) x(h(j(y(b(z))))) -> x(h(z)) d(y(b(c(z)))) -> e(y(b(c(z)))) SUCCESS Search time: 0.28 seconds |
7.91
OutputCOMPLETE SYSTEM: j(f(z)) -> z w(e(z)) -> h(j(z)) g(z) -> y(b(z)) i(y(z)) -> a(z) x(w(d(z))) -> x(w(i(z))) u(b(c(z))) -> o(z) x(w(a(z))) -> u(z) a(b(c(z))) -> e(f(c(z))) d(y(b(c(z)))) -> e(y(b(c(z)))) x(h(j(y(b(z))))) -> x(h(z)) x(h(c(z))) -> o(z) STATISTICS: General number of iterations: 17 number of nodes: 98 number of processes: 402 time for orient: 6.51 time for rewrite: 0.23 time for deduce: 0.07 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.418529 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.01 Process Killing killed 1 exceeding best by: 71% required time: 0.01 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 915 (yes: 861, timeouts: 0) time limit for check: 2.00 termination time: 6.21 Deduction critical pair criterion: all redundant CPs in total: 18 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.008631 Two: 0.000000 COMPLETE SYSTEM: j(f(z)) -> z w(e(z)) -> h(j(z)) g(z) -> y(b(z)) i(y(z)) -> a(z) x(w(d(z))) -> x(w(i(z))) u(b(c(z))) -> o(z) x(w(a(z))) -> u(z) a(b(c(z))) -> e(f(c(z))) d(y(b(c(z)))) -> e(y(b(c(z)))) x(h(j(y(b(z))))) -> x(h(z)) x(h(c(z))) -> o(z) |
3.91 |
BD94_collapse |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 7 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) |
0.00
OutputEQUATIONS:
Completion of BD94_collapse
c() = a() g(x) = x f(x,b()) = x f(x,g(y)) = f(g(x),y) f(b(),z) = c() COMPLETE TRS: RULES: c() -> a() g(x) -> x b() -> a() f(x,a()) -> x f(a(),x) -> a() SUCCESS Search time: 0.00 seconds |
0.02
OutputCOMPLETE SYSTEM: g(x) -> x f(x,b()) -> x a() -> b() c() -> b() f(b(),x) -> b() STATISTICS: General number of iterations: 8 number of nodes: 14 number of processes: 3 time for orient: 0.01 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 12 (yes: 12, timeouts: 0) time limit for check: 2.00 termination time: 0.01 Deduction critical pair criterion: all redundant CPs in total: 1 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000137 Two: 0.000000 COMPLETE SYSTEM: g(x) -> x f(x,b()) -> x a() -> b() c() -> b() f(b(),x) -> b() |
1.24 |
BD94_peano |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 4 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)) |
0.00
OutputEQUATIONS:
Completion of BD94_peano
plus(x,0()) = x plus(x,s(y)) = s(plus(x,y)) times(x,0()) = 0() times(x,s(y)) = plus(times(x,y),x) COMPLETE TRS: RULES: plus(x,0()) -> x plus(x,s(y)) -> s(plus(x,y)) times(x,0()) -> 0() times(x,s(y)) -> plus(times(x,y),x) SUCCESS Search time: 0.00 seconds |
0.02
OutputCOMPLETE SYSTEM: +(x,0()) -> x *(x,0()) -> 0() +(x,s(y)) -> s(+(x,y)) *(x,s(y)) -> +(*(x,y),x) STATISTICS: General number of iterations: 5 number of nodes: 10 number of processes: 3 time for orient: 0.02 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 8 (yes: 8, timeouts: 0) time limit for check: 2.00 termination time: 0.02 Deduction critical pair criterion: all redundant CPs in total: 6 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000082 Two: 0.000000 COMPLETE SYSTEM: +(x,0()) -> x *(x,0()) -> 0() +(x,s(y)) -> s(+(x,y)) *(x,s(y)) -> +(*(x,y),x) |
1.65 |
BD94_sqrt |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 6 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 BD94_sqrt
(RULES sqrt(0) → 0+(0,0) → 0i(0) → 0sqrt(+(i(x),x)) → 0) |
0.00
OutputEQUATIONS:
Completion of BD94_sqrt
i(0()) = 0() sqrt(plus(i(x),x)) = 0() plus(i(0()),0()) = 0() COMPLETE TRS: RULES: i(0()) -> 0() sqrt(plus(i(x),x)) -> 0() sqrt(0()) -> 0() plus(0(),0()) -> 0() SUCCESS Search time: 0.00 seconds |
0.01
OutputCOMPLETE SYSTEM: i(0()) -> 0() +(0(),0()) -> 0() sqrt(+(i(x),x)) -> 0() sqrt(0()) -> 0() STATISTICS: General number of iterations: 5 number of nodes: 6 number of processes: 0 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 4 (yes: 4, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 1 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000085 Two: 0.000000 COMPLETE SYSTEM: i(0()) -> 0() +(0(),0()) -> 0() sqrt(+(i(x),x)) -> 0() sqrt(0()) -> 0() |
1.25 |
BGK94_D08 |
26.32
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 12 equalities: 145 restarts: 0 time/cache: 0 time/set ops: 0.024 time/maxk: 24.835 time/normalization: 0.897 time/overlaps: 0.263 time/orientation constraints: 0.041 time/project: 0 time/sat: 0.671 time/update context: 0.44 Convergent TRS(VAR x y z)
Completion of BGK94_D08
(RULES f(x,i(x)) → f(b,b)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)) → bi(b) → bf(a,f(a,b)) → f(b,f(a,a))f(a,f(b,f(a,x))) → f(b,x)f(a,f(a,f(b,x))) → f(b,f(a,f(a,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,f(x,f(i(x),y)) → y,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)) |
0.30
OutputEQUATIONS:
Completion of BGK94_D08
f(x,f(y,z)) = f(f(x,y),z) f(x,i(x)) = e() f(x,e()) = x f(a(),f(a(),f(a(),a()))) = e() f(b(),b()) = e() f(a(),b()) = f(b(),i(a())) COMPLETE TRS: RULES: f(x,i(x)) -> e() f(x,e()) -> x f(b(),b()) -> e() f(b(),f(b(),x)) -> x i(e()) -> e() f(i(x),f(x,y)) -> y f(i(x),x) -> e() f(a(),f(a(),a())) -> f(b(),f(a(),b())) f(a(),f(a(),b())) -> f(b(),f(a(),a())) f(f(x,y),z) -> f(x,f(y,z)) f(y,f(i(y),x)) -> x f(a(),f(b(),a())) -> b() i(b()) -> b() i(i(x)) -> x i(a()) -> f(b(),f(a(),b())) f(e(),x) -> x i(f(y,x)) -> f(i(x),i(y)) f(a(),f(b(),f(a(),x))) -> f(b(),x) f(a(),f(a(),f(a(),x))) -> f(b(),f(a(),f(b(),x))) f(a(),f(a(),f(b(),x))) -> f(b(),f(a(),f(a(),x))) SUCCESS Search time: 0.30 seconds |
24.48
OutputCOMPLETE SYSTEM: e() -> f(b(),b()) f(a(),b()) -> f(b(),i(a())) f(x,f(y,z)) -> f(f(x,y),z) f(x,i(x)) -> f(b(),b()) f(f(x,b()),b()) -> x f(f(x,y),i(y)) -> x f(i(x),x) -> f(b(),b()) i(b()) -> b() f(f(x,i(y)),y) -> x f(f(x,a()),b()) -> f(f(x,b()),i(a())) f(f(b(),b()),x) -> x i(i(x)) -> x f(i(a()),b()) -> f(b(),a()) f(f(a(),a()),a()) -> i(a()) f(i(a()),i(a())) -> f(a(),a()) i(f(x,y)) -> f(i(y),i(x)) f(f(x,i(a())),b()) -> f(f(x,b()),a()) f(f(f(x,a()),a()),a()) -> f(x,i(a())) f(f(x,i(a())),i(a())) -> f(f(x,a()),a()) STATISTICS: General number of iterations: 96 number of nodes: 2485 number of processes: 72 time for orient: 14.44 time for rewrite: 1.07 time for deduce: 2.39 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.12 Process Killing killed 158 exceeding best by: 71% required time: 0.01 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 1716 (yes: 1292, timeouts: 0) time limit for check: 2.00 termination time: 13.33 Deduction critical pair criterion: all redundant CPs in total: 1287 for successful process: 13 required time: 0.15 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.02 overlaps: 0.02 maintenance: 0.00 One: 0.075516 Two: 0.000000 COMPLETE SYSTEM: e() -> f(b(),b()) f(a(),b()) -> f(b(),i(a())) f(x,f(y,z)) -> f(f(x,y),z) f(x,i(x)) -> f(b(),b()) f(f(x,b()),b()) -> x f(f(x,y),i(y)) -> x f(i(x),x) -> f(b(),b()) i(b()) -> b() f(f(x,i(y)),y) -> x f(f(x,a()),b()) -> f(f(x,b()),i(a())) f(f(b(),b()),x) -> x i(i(x)) -> x f(i(a()),b()) -> f(b(),a()) f(f(a(),a()),a()) -> i(a()) f(i(a()),i(a())) -> f(a(),a()) i(f(x,y)) -> f(i(y),i(x)) f(f(x,i(a())),b()) -> f(f(x,b()),a()) f(f(f(x,a()),a()),a()) -> f(x,i(a())) f(f(x,i(a())),i(a())) -> f(f(x,a()),a()) |
5.93 |
BGK94_D10 |
26.17
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 11 equalities: 138 restarts: 0 time/cache: 0 time/set ops: 0.036 time/maxk: 24.43 time/normalization: 1.011 time/overlaps: 0.327 time/orientation constraints: 0.043 time/project: 0 time/sat: 0.802 time/update context: 0.603 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,a)) → f(b,f(a,f(a,b)))f(a,f(a,f(a,x))) → f(b,f(a,f(a,f(b,x))))i(f(x,y)) → f(i(y),i(x))f(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,) |
0.27
OutputEQUATIONS:
Completion of BGK94_D10
f(x,f(y,z)) = f(f(x,y),z) f(x,i(x)) = e() f(x,e()) = x f(a(),f(a(),f(a(),f(a(),a())))) = e() f(b(),b()) = e() f(a(),b()) = f(b(),i(a())) COMPLETE TRS: RULES: f(x,i(x)) -> e() f(x,e()) -> x f(b(),b()) -> e() f(b(),f(b(),x)) -> x f(a(),f(b(),a())) -> b() i(b()) -> b() i(i(x)) -> x i(e()) -> e() f(i(x),x) -> e() f(i(x),f(x,y)) -> y f(a(),f(a(),a())) -> f(b(),f(a(),f(a(),b()))) f(f(x,y),z) -> f(x,f(y,z)) f(y,f(i(y),x)) -> x i(a()) -> f(b(),f(a(),b())) f(a(),f(b(),f(a(),x))) -> f(b(),x) f(e(),x) -> x i(f(y,x)) -> f(i(x),i(y)) f(a(),f(a(),f(a(),x))) -> f(b(),f(a(),f(a(),f(b(),x)))) SUCCESS Search time: 0.27 seconds |
7.56
OutputCOMPLETE SYSTEM: f(x,e()) -> x f(b(),b()) -> e() f(b(),i(a())) -> f(a(),b()) f(x,i(x)) -> e() f(f(x,y),z) -> f(x,f(y,z)) f(b(),f(i(a()),x)) -> f(a(),f(b(),x)) i(b()) -> b() i(e()) -> e() f(i(x),x) -> e() f(e(),x) -> x i(i(x)) -> x f(i(x),f(x,y)) -> y f(b(),a()) -> f(i(a()),b()) f(b(),f(a(),x)) -> f(i(a()),f(b(),x)) f(b(),f(b(),x)) -> x f(x,f(i(x),y)) -> y i(f(x,y)) -> f(i(y),i(x)) f(a(),f(a(),a())) -> f(i(a()),i(a())) f(a(),f(a(),f(a(),x))) -> f(i(a()),f(i(a()),x)) f(i(a()),f(i(a()),i(a()))) -> f(a(),a()) f(i(a()),f(i(a()),f(i(a()),x))) -> f(a(),f(a(),x)) STATISTICS: General number of iterations: 95 number of nodes: 1730 number of processes: 2 time for orient: 4.35 time for rewrite: 0.36 time for deduce: 0.83 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.05 Process Killing killed 81 exceeding best by: 71% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 711 (yes: 627, timeouts: 0) time limit for check: 2.00 termination time: 4.16 Deduction critical pair criterion: all redundant CPs in total: 1071 for successful process: 40 required time: 0.05 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.02 overlaps: 0.02 maintenance: 0.00 One: 0.023913 Two: 0.000000 COMPLETE SYSTEM: f(x,e()) -> x f(b(),b()) -> e() f(b(),i(a())) -> f(a(),b()) f(x,i(x)) -> e() f(f(x,y),z) -> f(x,f(y,z)) f(b(),f(i(a()),x)) -> f(a(),f(b(),x)) i(b()) -> b() i(e()) -> e() f(i(x),x) -> e() f(e(),x) -> x i(i(x)) -> x f(i(x),f(x,y)) -> y f(b(),a()) -> f(i(a()),b()) f(b(),f(a(),x)) -> f(i(a()),f(b(),x)) f(b(),f(b(),x)) -> x f(x,f(i(x),y)) -> y i(f(x,y)) -> f(i(y),i(x)) f(a(),f(a(),a())) -> f(i(a()),i(a())) f(a(),f(a(),f(a(),x))) -> f(i(a()),f(i(a()),x)) f(i(a()),f(i(a()),i(a()))) -> f(a(),a()) f(i(a()),f(i(a()),f(i(a()),x))) -> f(a(),f(a(),x)) |
6.13 |
BGK94_D12 |
29.96
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 12 equalities: 154 restarts: 0 time/cache: 0 time/set ops: 0.03 time/maxk: 28.178 time/normalization: 1.149 time/overlaps: 0.232 time/orientation constraints: 0.045 time/project: 0 time/sat: 0.843 time/update context: 0.495 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(x,f(i(x),y)) → y,f(i(x),x) → ei(b) → bi(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))))))i(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(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,) |
0.41
OutputEQUATIONS:
Completion of BGK94_D12
f(x,f(y,z)) = f(f(x,y),z) f(x,i(x)) = e() f(x,e()) = x f(a(),f(a(),f(a(),f(a(),f(a(),a()))))) = e() f(b(),b()) = e() f(a(),b()) = f(b(),i(a())) COMPLETE TRS: RULES: f(x,i(x)) -> e() f(x,e()) -> x f(b(),b()) -> e() f(b(),f(b(),x)) -> x f(a(),f(b(),a())) -> b() i(b()) -> b() i(i(x)) -> x i(e()) -> e() f(i(x),x) -> e() f(i(x),f(x,y)) -> y f(a(),f(a(),f(a(),a()))) -> f(b(),f(a(),f(a(),b()))) f(a(),f(a(),f(a(),b()))) -> f(b(),f(a(),f(a(),a()))) f(a(),f(a(),f(a(),f(b(),x)))) -> f(b(),f(a(),f(a(),f(a(),x)))) f(f(x,y),z) -> f(x,f(y,z)) f(y,f(i(y),x)) -> x i(a()) -> f(b(),f(a(),b())) f(a(),f(b(),f(a(),x))) -> f(b(),x) f(e(),x) -> x i(f(y,x)) -> f(i(x),i(y)) f(a(),f(a(),f(a(),f(a(),x)))) -> f(b(),f(a(),f(a(),f(b(),x)))) SUCCESS Search time: 0.41 seconds |
8.19
OutputCOMPLETE SYSTEM: f(x,e()) -> x f(b(),b()) -> e() f(b(),i(a())) -> f(a(),b()) f(x,i(x)) -> e() f(f(x,y),z) -> f(x,f(y,z)) f(b(),f(i(a()),x)) -> f(a(),f(b(),x)) i(b()) -> b() i(e()) -> e() f(i(x),x) -> e() f(e(),x) -> x i(i(x)) -> x f(i(x),f(x,y)) -> y f(b(),a()) -> f(i(a()),b()) f(b(),f(a(),x)) -> f(i(a()),f(b(),x)) f(b(),f(b(),x)) -> x f(x,f(i(x),y)) -> y i(f(x,y)) -> f(i(y),i(x)) f(a(),f(a(),a())) -> f(i(a()),f(i(a()),i(a()))) f(a(),f(a(),f(a(),f(a(),x)))) -> f(i(a()),f(i(a()),x)) f(i(a()),f(i(a()),f(i(a()),x))) -> f(a(),f(a(),f(a(),x))) STATISTICS: General number of iterations: 95 number of nodes: 1864 number of processes: 11 time for orient: 4.60 time for rewrite: 0.39 time for deduce: 0.95 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.06 Process Killing killed 81 exceeding best by: 71% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 725 (yes: 644, timeouts: 0) time limit for check: 2.00 termination time: 4.40 Deduction critical pair criterion: all redundant CPs in total: 1100 for successful process: 40 required time: 0.05 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.02 overlaps: 0.02 maintenance: 0.00 One: 0.024482 Two: 0.000000 COMPLETE SYSTEM: f(x,e()) -> x f(b(),b()) -> e() f(b(),i(a())) -> f(a(),b()) f(x,i(x)) -> e() f(f(x,y),z) -> f(x,f(y,z)) f(b(),f(i(a()),x)) -> f(a(),f(b(),x)) i(b()) -> b() i(e()) -> e() f(i(x),x) -> e() f(e(),x) -> x i(i(x)) -> x f(i(x),f(x,y)) -> y f(b(),a()) -> f(i(a()),b()) f(b(),f(a(),x)) -> f(i(a()),f(b(),x)) f(b(),f(b(),x)) -> x f(x,f(i(x),y)) -> y i(f(x,y)) -> f(i(y),i(x)) f(a(),f(a(),a())) -> f(i(a()),f(i(a()),i(a()))) f(a(),f(a(),f(a(),f(a(),x)))) -> f(i(a()),f(i(a()),x)) f(i(a()),f(i(a()),f(i(a()),x))) -> f(a(),f(a(),f(a(),x))) |
6.99 |
BGK94_D16 |
111.10
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 26 equalities: 176 restarts: 1 time/cache: 0 time/set ops: 0.052 time/maxk: 107.642 time/normalization: 2.162 time/overlaps: 0.586 time/orientation constraints: 2.387 time/project: 0 time/sat: 53.072 time/update context: 0.888 Convergent TRS(VAR x y z)
Completion of BGK94_D16
(RULES f(b,b) → ef(x,i(x)) → ef(i(x),x) → ef(a,f(b,a)) → bf(a,f(b,f(a,x))) → f(b,x)i(b) → bf(a,f(a,f(a,f(a,f(a,x))))) → f(b,f(a,f(a,f(a,f(b,x)))))f(b,f(a,f(a,f(a,a)))) → f(a,f(a,f(a,f(a,b))))f(b,f(a,f(a,f(a,f(a,x))))) → f(a,f(a,f(a,f(a,f(b,x)))))f(a,f(a,f(a,f(a,a)))) → f(b,f(a,f(a,f(a,b))))i(f(x,y)) → f(i(y),i(x))i(e) → ef(e,x) → x,f(i(x),f(x,y)) → y,i(i(x)) → x,f(b,f(b,x)) → x,f(x,f(i(x),y)) → y,i(a) → f(b,f(a,b))f(f(x,y),z) → f(x,f(y,z))f(x,e) → x,) |
13.22
OutputEQUATIONS:
Completion of BGK94_D16
f(x,f(y,z)) = f(f(x,y),z) f(x,i(x)) = e() f(x,e()) = x f(a(),f(a(),f(a(),f(a(),f(a(),f(a(),f(a(),a()))))))) = e() f(b(),b()) = e() f(a(),b()) = f(b(),i(a())) COMPLETE TRS: RULES: f(x,i(x)) -> f(a(),f(a(),f(a(),f(a(),f(a(),f(a(),f(a(),a()))))))) f(b(),b()) -> f(a(),f(a(),f(a(),f(a(),f(a(),f(a(),f(a(),a()))))))) f(x,f(a(),f(a(),f(a(),f(a(),f(a(),f(a(),f(a(),a())))))))) -> x f(i(x),f(x,y)) -> y f(i(x),x) -> 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()))))))) f(b(),f(b(),x)) -> x f(y,f(i(y),x)) -> x i(b()) -> b() i(i(x)) -> x i(f(y,x)) -> f(i(x),i(y)) f(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())))))) SUCCESS Search time: 13.22 seconds |
8.24
OutputCOMPLETE SYSTEM: f(x,e()) -> x f(b(),b()) -> e() f(b(),i(a())) -> f(a(),b()) f(x,i(x)) -> e() f(f(x,y),z) -> f(x,f(y,z)) f(b(),f(i(a()),x)) -> f(a(),f(b(),x)) i(b()) -> b() i(e()) -> e() f(i(x),x) -> e() f(e(),x) -> x i(i(x)) -> x f(i(x),f(x,y)) -> y f(b(),a()) -> f(i(a()),b()) f(b(),f(a(),x)) -> f(i(a()),f(b(),x)) f(b(),f(b(),x)) -> x f(x,f(i(x),y)) -> y i(f(x,y)) -> f(i(y),i(x)) f(a(),f(a(),f(a(),a()))) -> f(i(a()),f(i(a()),f(i(a()),i(a())))) f(a(),f(a(),f(a(),f(a(),f(a(),x))))) -> f(i(a()),f(i(a()),f(i(a()),x))) f(i(a()),f(i(a()),f(i(a()),f(i(a()),x)))) -> f(a(),f(a(),f(a(),f(a(),x)))) STATISTICS: General number of iterations: 96 number of nodes: 2028 number of processes: 11 time for orient: 4.68 time for rewrite: 0.44 time for deduce: 0.92 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.06 Process Killing killed 81 exceeding best by: 71% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 733 (yes: 649, timeouts: 0) time limit for check: 2.00 termination time: 4.49 Deduction critical pair criterion: all redundant CPs in total: 1112 for successful process: 40 required time: 0.05 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.02 overlaps: 0.02 maintenance: 0.00 One: 0.026130 Two: 0.000000 COMPLETE SYSTEM: f(x,e()) -> x f(b(),b()) -> e() f(b(),i(a())) -> f(a(),b()) f(x,i(x)) -> e() f(f(x,y),z) -> f(x,f(y,z)) f(b(),f(i(a()),x)) -> f(a(),f(b(),x)) i(b()) -> b() i(e()) -> e() f(i(x),x) -> e() f(e(),x) -> x i(i(x)) -> x f(i(x),f(x,y)) -> y f(b(),a()) -> f(i(a()),b()) f(b(),f(a(),x)) -> f(i(a()),f(b(),x)) f(b(),f(b(),x)) -> x f(x,f(i(x),y)) -> y i(f(x,y)) -> f(i(y),i(x)) f(a(),f(a(),f(a(),a()))) -> f(i(a()),f(i(a()),f(i(a()),i(a())))) f(a(),f(a(),f(a(),f(a(),f(a(),x))))) -> f(i(a()),f(i(a()),f(i(a()),x))) f(i(a()),f(i(a()),f(i(a()),f(i(a()),x)))) -> f(a(),f(a(),f(a(),f(a(),x)))) |
91.58 |
BGK94_M08 |
1.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 4 equalities: 89 restarts: 0 time/cache: 0 time/set ops: 0.012 time/maxk: 0.83 time/normalization: 0.069 time/overlaps: 0.033 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.018 time/update context: 0.047 Convergent TRS(VAR x y)
Completion of BGK94_M08
(RULES g(x,y) → f8(y)f7(x) → f8(x)f6(x) → f8(x)f5(x) → f8(x)f8(j(x)) → f8(f8(x))f2(x) → f8(x)f3(x) → f8(x)f4(x) → f8(x)f1(x) → f8(x)f8(f8(f8(f8(x)))) → f8(x)) |
0.11
OutputEQUATIONS:
Completion of BGK94_M08
g(g(x,y),j(z)) = g(x,g(y,z)) g(g(x,y),z) = g(x,z) g(f1(x),y) = f1(y) g(f2(x),y) = f2(y) g(f3(x),y) = f3(y) g(f4(x),y) = f4(y) g(f5(x),y) = f5(y) g(f6(x),y) = f6(y) g(f7(x),y) = f7(y) g(f8(x),y) = f8(y) g(x,j(f1(f2(x)))) = f2(x) g(x,j(f2(f3(x)))) = f3(x) g(x,j(f3(f4(x)))) = f4(x) g(x,j(f4(f5(x)))) = f5(x) g(x,j(f5(f6(x)))) = f6(x) g(x,j(f6(f7(x)))) = f7(x) g(x,j(f7(f8(x)))) = f8(x) g(x,j(f8(f1(x)))) = f1(x) COMPLETE TRS: RULES: f1(j(j(j(x)))) -> f1(x) f1(j(j(f1(x)))) -> f1(x) f1(j(f1(x))) -> f1(j(j(x))) g(y,x) -> f1(x) f2(x) -> f1(x) f3(x) -> f1(x) f4(x) -> f1(x) f5(x) -> f1(x) f6(x) -> f1(x) f7(x) -> f1(x) f8(x) -> f1(x) f1(f1(x)) -> f1(j(x)) SUCCESS Search time: 0.11 seconds |
⊥ | 2.38 |
BGK94_M10 |
1.53
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 4 equalities: 93 restarts: 0 time/cache: 0 time/set ops: 0.028 time/maxk: 1.155 time/normalization: 0.141 time/overlaps: 0.078 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.029 time/update context: 0.075 Convergent TRS(VAR x y)
Completion of BGK94_M10
(RULES g(x,y) → f10(y)f9(x) → f10(x)f10(j(x)) → f10(f10(x))f5(x) → f10(x)f8(x) → f10(x)f1(x) → f10(x)f7(x) → f10(x)f2(x) → f10(x)f3(x) → f10(x)f4(x) → f10(x)f6(x) → f10(x)f10(f10(f10(f10(x)))) → f10(x)) |
0.58
OutputEQUATIONS:
Completion of BGK94_M10
g(g(x,y),j(z)) = g(x,g(y,z)) g(g(x,y),z) = g(x,z) g(f1(x),y) = f1(y) g(f2(x),y) = f2(y) g(f3(x),y) = f3(y) g(f4(x),y) = f4(y) g(f5(x),y) = f5(y) g(f6(x),y) = f6(y) g(f7(x),y) = f7(y) g(f8(x),y) = f8(y) g(f9(x),y) = f9(y) g(f10(x),y) = f10(y) g(x,j(f1(f2(x)))) = f2(x) g(x,j(f2(f3(x)))) = f3(x) g(x,j(f3(f4(x)))) = f4(x) g(x,j(f4(f5(x)))) = f5(x) g(x,j(f5(f6(x)))) = f6(x) g(x,j(f6(f7(x)))) = f7(x) g(x,j(f7(f8(x)))) = f8(x) g(x,j(f8(f9(x)))) = f9(x) g(x,j(f9(f10(x)))) = f10(x) g(x,j(f10(f1(x)))) = f1(x) COMPLETE TRS: RULES: f9(j(j(j(x)))) -> f9(x) f9(j(j(f9(x)))) -> f9(x) f9(j(f9(x))) -> f9(j(j(x))) g(y,x) -> f9(x) f2(x) -> f9(x) f3(x) -> f9(x) f4(x) -> f9(x) f5(x) -> f9(x) f6(x) -> f9(x) f7(x) -> f9(x) f8(x) -> f9(x) f1(x) -> f9(x) f10(x) -> f9(x) f9(f9(x)) -> f9(j(x)) SUCCESS Search time: 0.58 seconds |
⊥ | 2.58 |
BGK94_M12 |
4.52
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 6 equalities: 126 restarts: 0 time/cache: 0 time/set ops: 0.045 time/maxk: 3.874 time/normalization: 0.222 time/overlaps: 0.094 time/orientation constraints: 0.018 time/project: 0 time/sat: 0.098 time/update context: 0.176 Convergent TRS(VAR x y)
Completion of BGK94_M12
(RULES g(x,y) → f3(y)f2(x) → f3(x)f8(x) → f3(x)f1(x) → f3(x)f5(x) → f3(x)f3(j(x)) → f3(f3(x))f4(x) → f3(x)f3(f3(f3(f3(x)))) → f3(x)f7(x) → f3(x)f6(x) → f3(x)f10(x) → f3(x)f12(x) → f3(x)f9(x) → f3(x)f11(x) → f3(x)) |
13.46
OutputEQUATIONS:
Completion of BGK94_M12
g(g(x,y),j(z)) = g(x,g(y,z)) g(g(x,y),z) = g(x,z) g(f1(x),y) = f1(y) g(f2(x),y) = f2(y) g(f3(x),y) = f3(y) g(f4(x),y) = f4(y) g(f5(x),y) = f5(y) g(f6(x),y) = f6(y) g(f7(x),y) = f7(y) g(f8(x),y) = f8(y) g(f9(x),y) = f9(y) g(f10(x),y) = f10(y) g(f11(x),y) = f11(y) g(f12(x),y) = f12(y) g(x,j(f1(f2(x)))) = f2(x) g(x,j(f2(f3(x)))) = f3(x) g(x,j(f3(f4(x)))) = f4(x) g(x,j(f4(f5(x)))) = f5(x) g(x,j(f5(f6(x)))) = f6(x) g(x,j(f6(f7(x)))) = f7(x) g(x,j(f7(f8(x)))) = f8(x) g(x,j(f8(f9(x)))) = f9(x) g(x,j(f9(f10(x)))) = f10(x) g(x,j(f10(f11(x)))) = f11(x) g(x,j(f11(f12(x)))) = f12(x) g(x,j(f12(f1(x)))) = f1(x) COMPLETE TRS: RULES: f11(j(x)) -> f11(f11(x)) f11(f11(f11(f11(x)))) -> f11(x) g(y,x) -> f11(x) f2(x) -> f11(x) f3(x) -> f11(x) f4(x) -> f11(x) f5(x) -> f11(x) f6(x) -> f11(x) f7(x) -> f11(x) f8(x) -> f11(x) f1(x) -> f11(x) f9(x) -> f11(x) f12(x) -> f11(x) f10(x) -> f11(x) SUCCESS Search time: 13.46 seconds |
⊥ | 2.83 |
BGK94_M14 |
3.60
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 5 equalities: 112 restarts: 0 time/cache: 0 time/set ops: 0.073 time/maxk: 2.888 time/normalization: 0.267 time/overlaps: 0.082 time/orientation constraints: 0.012 time/project: 0 time/sat: 0.053 time/update context: 0.178 Convergent TRS(VAR x y)
Completion of BGK94_M14
(RULES g(x,y) → f14(y)f4(x) → f14(x)f8(x) → f14(x)f9(x) → f14(x)f13(x) → f14(x)f12(x) → f14(x)f11(x) → f14(x)f3(x) → f14(x)f5(x) → f14(x)f6(x) → f14(x)f7(x) → f14(x)f10(x) → f14(x)f1(x) → f14(x)f14(j(x)) → f14(f14(x))f2(x) → f14(x)f14(f14(f14(f14(x)))) → f14(x)) |
⊥ | ⊥ | 3.07 |
BGK94_Z22W | ∞ | ⊥ | ⊥ | 439.43 |
BH96_fac8_theory |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 6 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 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)
Completion of BH96_fac8_theory
(RULES +(x,s(y)) → s(+(x,y))+(x,0) → x,*(x,0) → 0*(x,s(y)) → +(*(x,y),x)fac(0) → s(0)fac(s(x)) → *(s(x),fac(x))) |
0.00
OutputEQUATIONS:
Completion of BH96_fac8_theory
plus(x,0()) = x plus(x,s(y())) = s(plus(x,y())) times(x,0()) = 0() times(x,s(y())) = plus(times(x,y()),x) fac(0()) = s(0()) fac(s(x)) = times(s(x),fac(x)) COMPLETE TRS: RULES: plus(x,0()) -> x plus(x,s(y())) -> s(plus(x,y())) times(x,0()) -> 0() times(x,s(y())) -> plus(times(x,y()),x) fac(0()) -> s(0()) fac(s(x)) -> times(s(x),fac(x)) SUCCESS Search time: 0.00 seconds |
0.11
OutputCOMPLETE SYSTEM: fac(0()) -> s(0()) +(x,0()) -> x *(x,0()) -> 0() +(x,s(y())) -> s(+(x,y())) *(x,s(y())) -> +(*(x,y()),x) fac(s(x)) -> *(s(x),fac(x)) STATISTICS: General number of iterations: 7 number of nodes: 16 number of processes: 15 time for orient: 0.09 time for rewrite: 0.00 time for deduce: 0.01 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 34 (yes: 34, timeouts: 0) time limit for check: 2.00 termination time: 0.09 Deduction critical pair criterion: all redundant CPs in total: 8 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000155 Two: 0.000000 COMPLETE SYSTEM: fac(0()) -> s(0()) +(x,0()) -> x *(x,0()) -> 0() +(x,s(y())) -> s(+(x,y())) *(x,s(y())) -> +(*(x,y()),x) fac(s(x)) -> *(s(x),fac(x)) |
0.87 |
Chr89_A2 |
2.44
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 8 equalities: 109 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 2.143 time/normalization: 0.123 time/overlaps: 0.072 time/orientation constraints: 0.019 time/project: 0 time/sat: 0.067 time/update context: 0.07 Convergent TRS(VAR x y z)
Completion of Chr89_A2
(RULES f(x,i1(x)) → a1f(i1(x),a1) → i1(x)i2(x) → f(i1(x),a2)i1(f(x,y)) → f(i1(y),i1(x))f(i1(x),f(x,y)) → y,i1(i1(x)) → f(x,a1)i1(a1) → a1i1(a2) → a1f(x,f(i1(x),y)) → y,f(f(x,y),z) → f(x,f(y,z))f(a1,x) → x,f(a2,x) → x,) |
0.25
OutputEQUATIONS:
Completion of Chr89_A2
f(f(x,y),z) = f(x,f(y,z)) f(a1(),y) = y f(a2(),y) = y f(x,i1(x)) = a1() f(x,i2(x)) = a2() COMPLETE TRS: RULES: f(f(x,y),z) -> f(x,f(y,z)) f(a1(),y) -> y f(a2(),y) -> y f(x,i1(x)) -> a1() i1(a1()) -> a1() i1(a2()) -> a1() f(i1(x),a1()) -> i1(x) f(y,f(i1(y),x)) -> x i1(i1(x)) -> f(x,a1()) f(i1(y),f(y,x)) -> x i2(x) -> f(i1(x),a2()) i1(f(y,x)) -> f(i1(x),i1(y)) SUCCESS Search time: 0.25 seconds |
6.28
OutputCOMPLETE SYSTEM: f(a2(),x) -> x a1() -> i1(a2()) f(x,i2(x)) -> a2() i2(a2()) -> a2() f(f(x,y),z) -> f(x,f(y,z)) f(x,f(i2(x),y)) -> y f(x,a2()) -> i2(i2(x)) f(i2(i2(x)),y) -> f(x,y) f(i2(x),f(x,y)) -> y i2(i2(i2(x))) -> i2(x) i2(f(x,y)) -> f(i2(y),i2(x)) f(x,i1(x)) -> i1(a2()) f(x,i1(a2())) -> i1(i2(x)) i1(i2(i2(x))) -> i1(x) i2(i1(x)) -> i2(i2(x)) i1(i1(x)) -> i1(i2(x)) f(i1(x),y) -> f(i2(x),y) i1(f(x,y)) -> f(i2(y),i1(x)) STATISTICS: General number of iterations: 108 number of nodes: 2278 number of processes: 1 time for orient: 2.97 time for rewrite: 0.36 time for deduce: 0.78 Isomorphism Check: renamings+ (detected automatically) time for checking: 0.485787 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.05 Process Killing killed 39 exceeding best by: 71% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 450 (yes: 368, timeouts: 0) time limit for check: 2.00 termination time: 2.84 Deduction critical pair criterion: all redundant CPs in total: 1834 for successful process: 47 required time: 0.06 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.02 overlaps: 0.04 maintenance: 0.00 One: 0.015453 Two: 0.000000 COMPLETE SYSTEM: f(a2(),x) -> x a1() -> i1(a2()) f(x,i2(x)) -> a2() i2(a2()) -> a2() f(f(x,y),z) -> f(x,f(y,z)) f(x,f(i2(x),y)) -> y f(x,a2()) -> i2(i2(x)) f(i2(i2(x)),y) -> f(x,y) f(i2(x),f(x,y)) -> y i2(i2(i2(x))) -> i2(x) i2(f(x,y)) -> f(i2(y),i2(x)) f(x,i1(x)) -> i1(a2()) f(x,i1(a2())) -> i1(i2(x)) i1(i2(i2(x))) -> i1(x) i2(i1(x)) -> i2(i2(x)) i1(i1(x)) -> i1(i2(x)) f(i1(x),y) -> f(i2(x),y) i1(f(x,y)) -> f(i2(y),i1(x)) |
2.47 |
Chr89_A24 | ∞ | ⊥ | ⊥ | ∞ |
Chr89_A3 |
4.36
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 9 equalities: 139 restarts: 0 time/cache: 0 time/set ops: 0.012 time/maxk: 3.905 time/normalization: 0.182 time/overlaps: 0.132 time/orientation constraints: 0.028 time/project: 0 time/sat: 0.215 time/update context: 0.103 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,) |
1.21
OutputEQUATIONS:
Completion of Chr89_A3
f(f(x,y),z) = f(x,f(y,z)) f(a1(),y) = y f(a2(),y) = y f(a3(),y) = y f(x,i1(x)) = a1() f(x,i2(x)) = a2() f(x,i3(x)) = a3() COMPLETE TRS: RULES: f(f(x,y),z) -> f(x,f(y,z)) f(a1(),y) -> y f(a2(),y) -> y f(a3(),y) -> y f(x,i1(x)) -> a1() i1(a1()) -> a1() i1(a2()) -> a1() i1(a3()) -> a1() f(i1(x),f(x,y)) -> y i2(x) -> f(i1(x),a2()) i3(x) -> f(i1(x),a3()) f(y,f(i1(y),x)) -> x i1(i1(x)) -> f(x,a1()) i1(f(y,x)) -> f(i1(x),i1(y)) f(i1(x),a1()) -> i1(x) SUCCESS Search time: 1.21 seconds |
23.82
OutputCOMPLETE SYSTEM: f(a1(),x) -> x f(a2(),x) -> x f(a3(),x) -> x f(x,i1(x)) -> a1() i1(a3()) -> a1() i1(a2()) -> a1() i1(a1()) -> a1() f(f(x,y),z) -> f(x,f(y,z)) f(x,f(i1(x),y)) -> y f(x,a1()) -> i1(i1(x)) f(i1(i1(x)),y) -> f(x,y) f(i1(x),f(x,y)) -> y i3(x) -> f(i1(x),a3()) i1(i1(i1(x))) -> i1(x) i2(x) -> f(i1(x),a2()) i1(f(x,y)) -> f(i1(y),i1(x)) STATISTICS: General number of iterations: 66 number of nodes: 2113 number of processes: 92 time for orient: 12.70 time for rewrite: 1.00 time for deduce: 2.53 Isomorphism Check: renamings+ (detected automatically) time for checking: 2.369166 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.09 Process Killing killed 96 exceeding best by: 71% required time: 0.01 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 1534 (yes: 1199, timeouts: 0) time limit for check: 2.00 termination time: 11.84 Deduction critical pair criterion: all redundant CPs in total: 926 for successful process: 59 required time: 0.16 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.02 overlaps: 0.01 maintenance: 0.00 One: 0.055424 Two: 0.000000 COMPLETE SYSTEM: f(a1(),x) -> x f(a2(),x) -> x f(a3(),x) -> x f(x,i1(x)) -> a1() i1(a3()) -> a1() i1(a2()) -> a1() i1(a1()) -> a1() f(f(x,y),z) -> f(x,f(y,z)) f(x,f(i1(x),y)) -> y f(x,a1()) -> i1(i1(x)) f(i1(i1(x)),y) -> f(x,y) f(i1(x),f(x,y)) -> y i3(x) -> f(i1(x),a3()) i1(i1(i1(x))) -> i1(x) i2(x) -> f(i1(x),a2()) i1(f(x,y)) -> f(i1(y),i1(x)) |
5.84 |
HR94_1 | ∞ | ⊥ | ⊥ | ∞ |
HR94_2 | ∞ | ⊥ | ⊥ | ∞ |
KK99_linear_assoc |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 2 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 z)
Completion of KK99_linear_assoc
(RULES +(+(x,y),z) → +(x,+(y,z))f(+(x,y)) → +(f(x),f(y))) |
0.00
OutputEQUATIONS:
Completion of KK99_linear_assoc
plus(plus(x,y),z) = plus(x,plus(y,z)) f(plus(x,y)) = plus(f(x),f(y)) COMPLETE TRS: RULES: plus(plus(x,y),z) -> plus(x,plus(y,z)) f(plus(x,y)) -> plus(f(x),f(y)) SUCCESS Search time: 0.00 seconds |
0.02
OutputCOMPLETE SYSTEM: +(x,+(y,z)) -> +(+(x,y),z) f(+(x,y)) -> +(f(x),f(y)) STATISTICS: General number of iterations: 3 number of nodes: 14 number of processes: 3 time for orient: 0.02 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 6 (yes: 6, timeouts: 0) time limit for check: 2.00 termination time: 0.02 Deduction critical pair criterion: all redundant CPs in total: 6 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.002590 Two: 0.000000 COMPLETE SYSTEM: +(x,+(y,z)) -> +(+(x,y),z) f(+(x,y)) -> +(f(x),f(y)) |
2.04 |
LS06_CGE4 |
62.51
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 10 equalities: 122 restarts: 1 time/cache: 0 time/set ops: 0.045 time/maxk: 61.099 time/normalization: 0.478 time/overlaps: 0.409 time/orientation constraints: 1.115 time/project: 0 time/sat: 53.147 time/update context: 0.191 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 |
153.36
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 11 equalities: 149 restarts: 1 time/cache: 0 time/set ops: 0.103 time/maxk: 150.197 time/normalization: 1.125 time/overlaps: 1.062 time/orientation constraints: 1.517 time/project: 0 time/sat: 135.731 time/update context: 0.395 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 |
0.17
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 4 equalities: 35 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.109 time/normalization: 0.016 time/overlaps: 0.027 time/orientation constraints: 0.002 time/project: 0 time/sat: 0.009 time/update context: 0.006 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,) |
0.02
OutputEQUATIONS:
Completion of LS94_G0
f(x,f(y,z)) = f(f(x,y),z) f(x,i(x)) = e() f(i(x),x) = e() f(x,e()) = x f(e(),x) = x a(a(x)) = x b(b(x)) = x a(b(a(b(a(b(x)))))) = x COMPLETE TRS: RULES: f(x,i(x)) -> e() f(i(x),x) -> e() f(x,e()) -> x f(e(),x) -> x a(a(x)) -> x b(b(x)) -> x f(f(x,y),z) -> f(x,f(y,z)) i(e()) -> e() f(y,f(i(y),x)) -> x f(i(y),f(y,x)) -> x i(i(x)) -> x a(b(a(x))) -> b(a(b(x))) i(f(y,x)) -> f(i(x),i(y)) SUCCESS Search time: 0.02 seconds |
0.32
OutputCOMPLETE SYSTEM: f(x,e()) -> x f(e(),x) -> x a(a(x)) -> x b(b(x)) -> x f(x,i(x)) -> e() i(e()) -> e() f(i(x),x) -> e() f(f(x,y),z) -> f(x,f(y,z)) f(x,f(i(x),y)) -> y i(i(x)) -> x f(i(x),f(x,y)) -> y a(b(a(x))) -> b(a(b(x))) i(f(x,y)) -> f(i(y),i(x)) STATISTICS: General number of iterations: 23 number of nodes: 231 number of processes: 7 time for orient: 0.23 time for rewrite: 0.02 time for deduce: 0.04 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 47 (yes: 43, timeouts: 0) time limit for check: 2.00 termination time: 0.22 Deduction critical pair criterion: all redundant CPs in total: 152 for successful process: 15 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000355 Two: 0.000000 COMPLETE SYSTEM: f(x,e()) -> x f(e(),x) -> x a(a(x)) -> x b(b(x)) -> x f(x,i(x)) -> e() i(e()) -> e() f(i(x),x) -> e() f(f(x,y),z) -> f(x,f(y,z)) f(x,f(i(x),y)) -> y i(i(x)) -> x f(i(x),f(x,y)) -> y a(b(a(x))) -> b(a(b(x))) i(f(x,y)) -> f(i(y),i(x)) |
5.53 |
LS94_G1 | ∞ | ∞ | ⊥ | ∞ |
LS94_G2 | ∞ | ⊥ | ⊥ | ∞ |
LS94_G3 | ∞ | ⊥ | ⊥ | ∞ |
LS94_P1 |
292.49
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 24 equalities: 355 restarts: 0 time/cache: 0 time/set ops: 0.167 time/maxk: 282.433 time/normalization: 8.485 time/overlaps: 0.426 time/orientation constraints: 0.638 time/project: 0 time/sat: 15.12 time/update context: 8.464 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,T(x) → x,s(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,) |
15.58
OutputEQUATIONS:
Completion of LS94_P1
f(x,f(y,z)) = f(f(x,y),z) f(x,i(x)) = e() f(i(x),x) = e() f(e(),x) = x f(x,e()) = x T(r(t(R(R(x))))) = x R(s(r(S(S(x))))) = x S(t(s(T(T(x))))) = x r(R(x)) = x R(r(x)) = x s(S(x)) = x S(s(x)) = x t(T(x)) = x T(t(x)) = x COMPLETE TRS: RULES: f(x,i(x)) -> e() f(i(x),x) -> e() f(e(),x) -> x f(x,e()) -> x t(x) -> x S(x) -> x T(x) -> x f(f(x,y),z) -> f(x,f(y,z)) i(e()) -> e() f(y,f(i(y),x)) -> x f(i(y),f(y,x)) -> x i(i(x)) -> x i(f(y,x)) -> f(i(x),i(y)) s(x) -> x R(x) -> x r(x) -> x SUCCESS Search time: 15.58 seconds |
⊥ | 22.53 |
Les83_fib |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 9 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 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 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))) |
0.00
OutputEQUATIONS:
Completion of Les83_fib
plus(0(),x) = x plus(s(x),y) = s(plus(x,y)) plus(plus(x,y),z) = plus(x,plus(y,z)) fib(0()) = 0() fib(s(0())) = s(0()) fib(s(s(x))) = plus(fib(x),fib(s(x))) dfib(0(),y) = y dfib(s(0()),y) = s(y) dfib(s(s(x)),y) = dfib(s(x),dfib(x,y)) COMPLETE TRS: RULES: plus(0(),x) -> x plus(s(x),y) -> s(plus(x,y)) plus(plus(x,y),z) -> plus(x,plus(y,z)) fib(0()) -> 0() fib(s(0())) -> s(0()) fib(s(s(x))) -> plus(fib(x),fib(s(x))) dfib(0(),y) -> y dfib(s(0()),y) -> s(y) dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y)) SUCCESS Search time: 0.00 seconds |
0.17
OutputCOMPLETE SYSTEM: fib(0()) -> 0() +(0(),x) -> x fib(s(0())) -> s(0()) dfib(0(),x) -> x +(s(x),y) -> s(+(x,y)) dfib(s(0()),x) -> s(x) +(+(x,y),z) -> +(x,+(y,z)) fib(s(s(x))) -> +(fib(x),fib(s(x))) dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y)) STATISTICS: General number of iterations: 10 number of nodes: 50 number of processes: 14 time for orient: 0.13 time for rewrite: 0.01 time for deduce: 0.01 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 38 (yes: 35, timeouts: 0) time limit for check: 2.00 termination time: 0.13 Deduction critical pair criterion: all redundant CPs in total: 25 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000231 Two: 0.000000 COMPLETE SYSTEM: fib(0()) -> 0() +(0(),x) -> x fib(s(0())) -> s(0()) dfib(0(),x) -> x +(s(x),y) -> s(+(x,y)) dfib(s(0()),x) -> s(x) +(+(x,y),z) -> +(x,+(y,z)) fib(s(s(x))) -> +(fib(x),fib(s(x))) dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y)) |
3.80 |
Les83_subset |
0.02
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 12 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0.005 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)) |
0.00
OutputEQUATIONS:
Completion of Les83_subset
if(tt(),x,y) = x if(ff(),x,y) = y if(x,y,y) = y if(x,tt(),ff()) = x eq(0(),0()) = tt() eq(0(),s(x)) = ff() eq(s(x),0()) = ff() eq(s(x),s(y)) = eq(x,y) has(empty(),x) = ff() has(plus(u,x),y) = if(eq(x,y),tt(),has(u,y)) subset(empty(),v) = tt() subset(plus(u,x),v) = if(has(v,x),subset(u,v),ff()) COMPLETE TRS: RULES: if(tt(),x,y) -> x if(ff(),x,y) -> y if(x,y,y) -> y if(x,tt(),ff()) -> x eq(0(),0()) -> tt() eq(0(),s(x)) -> ff() eq(s(x),0()) -> ff() eq(s(x),s(y)) -> eq(x,y) has(empty(),x) -> ff() has(plus(u,x),y) -> if(eq(x,y),tt(),has(u,y)) subset(empty(),v) -> tt() subset(plus(u,x),v) -> if(has(v,x),subset(u,v),ff()) SUCCESS Search time: 0.00 seconds |
0.09
OutputCOMPLETE SYSTEM: eq(0(),0()) -> tt() has(empty(),x) -> ff() subset(empty(),x) -> tt() if(ff(),x,y) -> y if(x,y,y) -> y eq(0(),s(x)) -> ff() eq(s(x),0()) -> ff() if(tt(),x,y) -> x if(x,tt(),ff()) -> x eq(s(x),s(y)) -> eq(x,y) subset(+(x,y),u) -> if(has(u,y),subset(x,u),ff()) has(+(x,y),u) -> if(eq(y,u),tt(),has(x,u)) STATISTICS: General number of iterations: 13 number of nodes: 30 number of processes: 5 time for orient: 0.07 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 27 (yes: 25, timeouts: 0) time limit for check: 2.00 termination time: 0.06 Deduction critical pair criterion: all redundant CPs in total: 8 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000371 Two: 0.000000 COMPLETE SYSTEM: eq(0(),0()) -> tt() has(empty(),x) -> ff() subset(empty(),x) -> tt() if(ff(),x,y) -> y if(x,y,y) -> y eq(0(),s(x)) -> ff() eq(s(x),0()) -> ff() if(tt(),x,y) -> x if(x,tt(),ff()) -> x eq(s(x),s(y)) -> eq(x,y) subset(+(x,y),u) -> if(has(u,y),subset(x,u),ff()) has(+(x,y),u) -> if(eq(y,u),tt(),has(x,u)) |
3.87 |
OKW95_dt1_theory |
0.27
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 4 equalities: 72 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.213 time/normalization: 0.015 time/overlaps: 0.013 time/orientation constraints: 0.009 time/project: 0 time/sat: 0.004 time/update context: 0.011 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))fib(0) → s(0)p(s(x)) → x,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,) |
5.21
OutputEQUATIONS:
Completion of OKW95_dt1_theory
fib(0()) = s(0()) fib(s(0())) = s(0()) fib(s(s(x))) = plus(fib(s(x)),fib(x)) dfib(0()) = s(0()) dfib(s(0())) = s(0()) dfib(s(s(x))) = plus(dfib(s(x)),plus(dfib(x),dfib(x))) plus(x,s(y)) = s(plus(x,y)) plus(x,0()) = x minus(s(x),s(y)) = minus(x,y) minus(x,0()) = x p(x) = minus(x,s(0())) COMPLETE TRS: RULES: fib(0()) -> s(0()) fib(s(0())) -> s(0()) fib(s(s(x))) -> plus(fib(s(x)),fib(x)) dfib(0()) -> s(0()) dfib(s(0())) -> s(0()) dfib(s(s(x))) -> plus(dfib(s(x)),plus(dfib(x),dfib(x))) plus(x,s(y)) -> s(plus(x,y)) plus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) minus(x,0()) -> x minus(x,s(0())) -> p(x) p(s(x)) -> x SUCCESS Search time: 5.21 seconds |
0.75
OutputCOMPLETE SYSTEM: fib(0()) -> s(0()) dfib(0()) -> s(0()) +(x,0()) -> x -(x,0()) -> x fib(s(0())) -> s(0()) dfib(s(0())) -> s(0()) +(x,s(y)) -> s(+(x,y)) p(x) -> -(x,s(0())) -(s(x),s(y)) -> -(x,y) fib(s(s(x))) -> +(fib(s(x)),fib(x)) dfib(s(s(x))) -> +(dfib(s(x)),+(dfib(x),dfib(x))) STATISTICS: General number of iterations: 18 number of nodes: 103 number of processes: 55 time for orient: 0.64 time for rewrite: 0.02 time for deduce: 0.03 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 154 (yes: 140, timeouts: 0) time limit for check: 2.00 termination time: 0.62 Deduction critical pair criterion: all redundant CPs in total: 41 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.001154 Two: 0.000000 COMPLETE SYSTEM: fib(0()) -> s(0()) dfib(0()) -> s(0()) +(x,0()) -> x -(x,0()) -> x fib(s(0())) -> s(0()) dfib(s(0())) -> s(0()) +(x,s(y)) -> s(+(x,y)) p(x) -> -(x,s(0())) -(s(x),s(y)) -> -(x,y) fib(s(s(x))) -> +(fib(s(x)),fib(x)) dfib(s(s(x))) -> +(dfib(s(x)),+(dfib(x),dfib(x))) |
2.99 |
SK90_3.01 |
1.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 6 equalities: 70 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 0.77 time/normalization: 0.099 time/overlaps: 0.068 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.063 time/update context: 0.028 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))) |
0.03
OutputEQUATIONS:
Completion of SK90_3.01
times(one(),y) = y times(i(x),x) = one() times(times(x,y),z) = times(x,times(y,z)) divi(x,y) = times(x,i(y)) COMPLETE TRS: RULES: times(one(),y) -> y times(i(x),x) -> one() times(times(x,y),z) -> times(x,times(y,z)) divi(x,y) -> times(x,i(y)) times(x,times(i(x),y)) -> y i(one()) -> one() times(i(y),times(y,x)) -> x times(x,one()) -> x times(x,i(x)) -> one() i(i(x)) -> x i(times(y,x)) -> times(i(x),i(y)) SUCCESS Search time: 0.03 seconds |
1.27
OutputCOMPLETE SYSTEM: *(one(),y) -> y *(i(y),y) -> one() div(y,x) -> *(y,i(x)) *(*(y,x),z) -> *(y,*(x,z)) *(i(y),*(y,x)) -> x i(one()) -> one() i(i(y)) -> y *(y,i(y)) -> one() div(y,y) -> one() *(y,*(i(y),x)) -> x *(y,one()) -> y i(*(y,x)) -> *(i(x),i(y)) STATISTICS: General number of iterations: 44 number of nodes: 539 number of processes: 17 time for orient: 0.76 time for rewrite: 0.09 time for deduce: 0.14 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.01 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 153 (yes: 135, timeouts: 0) time limit for check: 2.00 termination time: 0.73 Deduction critical pair criterion: all redundant CPs in total: 373 for successful process: 13 required time: 0.01 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.01 maintenance: 0.00 One: 0.003805 Two: 0.000000 COMPLETE SYSTEM: *(one(),y) -> y *(i(y),y) -> one() div(y,x) -> *(y,i(x)) *(*(y,x),z) -> *(y,*(x,z)) *(i(y),*(y,x)) -> x i(one()) -> one() i(i(y)) -> y *(y,i(y)) -> one() div(y,y) -> one() *(y,*(i(y),x)) -> x *(y,one()) -> y i(*(y,x)) -> *(i(x),i(y)) |
5.51 |
SK90_3.02 |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 3 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))) |
0.00
OutputEQUATIONS:
Completion of SK90_3.02
f(f(x)) = x plus(f(x),f(y)) = f(plus(x,y)) plus(plus(x,y),z) = plus(x,plus(y,z)) COMPLETE TRS: RULES: f(f(x)) -> x plus(plus(x,y),z) -> plus(x,plus(y,z)) plus(f(x),y) -> f(plus(x,f(y))) SUCCESS Search time: 0.00 seconds |
0.02
OutputCOMPLETE SYSTEM: f(f(x)) -> x f(+(x,y)) -> +(f(x),f(y)) +(x,+(y,z)) -> +(+(x,y),z) STATISTICS: General number of iterations: 4 number of nodes: 16 number of processes: 1 time for orient: 0.02 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.000103 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 7 (yes: 7, timeouts: 0) time limit for check: 2.00 termination time: 0.01 Deduction critical pair criterion: all redundant CPs in total: 6 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000091 Two: 0.000000 COMPLETE SYSTEM: f(f(x)) -> x f(+(x,y)) -> +(f(x),f(y)) +(x,+(y,z)) -> +(+(x,y),z) |
2.88 |
SK90_3.03 |
5.31
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 10 equalities: 118 restarts: 1 time/cache: 0 time/set ops: 0.006 time/maxk: 4.94 time/normalization: 0.132 time/overlaps: 0.133 time/orientation constraints: 0.563 time/project: 0 time/sat: 2.076 time/update context: 0.067 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) |
0.54
OutputEQUATIONS:
Completion of SK90_3.03
d(d(x,x),d(d(y,y),y)) = y d(d(x,y),d(z,y)) = d(x,z) d(x,x) = one() d(one(),y) = i(y) d(x,i(y)) = times(x,y) COMPLETE TRS: RULES: i(i(x)) -> x times(x,i(x)) -> one() times(i(x),times(x,y)) -> y d(x,y) -> times(x,i(y)) times(x,times(i(x),y)) -> y i(one()) -> one() times(one(),x) -> x times(x,one()) -> x times(i(x),x) -> one() i(times(y,x)) -> times(i(x),i(y)) times(times(x,y),z) -> times(x,times(y,z)) SUCCESS Search time: 0.54 seconds |
5.72
OutputCOMPLETE SYSTEM: d(x,x) -> one() i(one()) -> one() i(i(x)) -> x *(one(),x) -> x *(x,one()) -> x *(x,*(y,z)) -> *(*(x,y),z) d(x,y) -> *(x,i(y)) *(i(x),x) -> one() *(x,i(x)) -> one() i(*(y,x)) -> *(i(x),i(y)) *(*(x,y),i(y)) -> x *(*(x,i(y)),y) -> x STATISTICS: General number of iterations: 69 number of nodes: 2925 number of processes: 18 time for orient: 2.58 time for rewrite: 0.57 time for deduce: 0.63 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.06 Process Killing killed 2 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 284 (yes: 218, timeouts: 0) time limit for check: 2.00 termination time: 2.42 Deduction critical pair criterion: all redundant CPs in total: 1682 for successful process: 23 required time: 0.09 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.03 overlaps: 0.03 maintenance: 0.00 One: 0.015224 Two: 0.000000 COMPLETE SYSTEM: d(x,x) -> one() i(one()) -> one() i(i(x)) -> x *(one(),x) -> x *(x,one()) -> x *(x,*(y,z)) -> *(*(x,y),z) d(x,y) -> *(x,i(y)) *(i(x),x) -> one() *(x,i(x)) -> one() i(*(y,x)) -> *(i(x),i(y)) *(*(x,y),i(y)) -> x *(*(x,i(y)),y) -> x |
10.42 |
SK90_3.04 |
1.90
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 7 equalities: 76 restarts: 0 time/cache: 0 time/set ops: 0.02 time/maxk: 1.368 time/normalization: 0.207 time/overlaps: 0.141 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.04 time/update context: 0.021 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)) |
0.68
OutputEQUATIONS:
Completion of SK90_3.04
times(times(x,y),z) = times(x,times(y,z)) times(one(),y) = y g(x) = times(f(x),x) times(g(x),y) = y COMPLETE TRS: RULES: times(times(x,y),z) -> times(x,times(y,z)) times(one(),y) -> y times(g(x),y) -> y times(f(x),times(x,y)) -> y times(f(one()),x) -> x times(f(f(x)),y) -> times(x,y) times(x,g(x)) -> x times(f(g(x)),y) -> y g(times(x,y)) -> g(y) times(f(x),x) -> g(x) times(y,times(f(y),x)) -> x g(one()) -> one() g(g(x)) -> g(x) g(f(x)) -> times(x,f(x)) times(f(times(y,x)),z) -> times(f(x),times(f(y),z)) SUCCESS Search time: 0.68 seconds |
0.83
OutputCOMPLETE SYSTEM: *(one(),x) -> x g(x) -> *(f(x),x) *(*(x,y),z) -> *(x,*(y,z)) *(f(x),*(x,y)) -> y *(f(one()),x) -> x *(x,*(f(x),y)) -> y *(f(f(x)),y) -> *(x,y) *(f(*(x,y)),z) -> *(f(y),*(f(x),z)) STATISTICS: General number of iterations: 40 number of nodes: 494 number of processes: 5 time for orient: 0.49 time for rewrite: 0.06 time for deduce: 0.13 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.01 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 103 (yes: 81, timeouts: 0) time limit for check: 2.00 termination time: 0.47 Deduction critical pair criterion: all redundant CPs in total: 475 for successful process: 63 required time: 0.01 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.01 maintenance: 0.00 One: 0.001867 Two: 0.000000 COMPLETE SYSTEM: *(one(),x) -> x g(x) -> *(f(x),x) *(*(x,y),z) -> *(x,*(y,z)) *(f(x),*(x,y)) -> y *(f(one()),x) -> x *(x,*(f(x),y)) -> y *(f(f(x)),y) -> *(x,y) *(f(*(x,y)),z) -> *(f(y),*(f(x),z)) |
17.65 |
SK90_3.05 |
25.08
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 32 equalities: 118 restarts: 2 time/cache: 0 time/set ops: 0.029 time/maxk: 18.933 time/normalization: 1.194 time/overlaps: 0.55 time/orientation constraints: 0.783 time/project: 0 time/sat: 1.347 time/update context: 0.498 Convergent TRS(VAR y x z)
Completion of SK90_3.05
(RULES *(y,g(y)) → g(y)f(g(y)) → g(y)f(*(y,x)) → g(y)*(f(y),y) → f(y)*(*(y,x),z) → *(f(x),z)g(*(y,x)) → f(x)f(f(y)) → f(y)*(y,f(x)) → *(y,x)g(f(y)) → f(y)*(y,*(x,z)) → *(y,g(x))g(g(y)) → g(y)*(f(y),g(y)) → y,*(g(y),x) → *(y,x)) |
0.17
OutputEQUATIONS:
Completion of SK90_3.05
times(times(x,y),times(y,z)) = y times(times(x,x),x) = f(x) times(x,times(x,x)) = g(x) times(g(x),y) = times(x,y) COMPLETE TRS: RULES: times(g(x),y) -> times(x,y) times(f(x),g(x)) -> x times(x,g(x)) -> g(x) times(f(x),x) -> f(x) f(f(x)) -> f(x) times(x,times(y,z)) -> times(x,g(y)) g(times(x,y)) -> f(y) g(g(x)) -> g(x) g(f(x)) -> f(x) f(g(x)) -> g(x) f(times(x,y)) -> g(x) times(x,f(y)) -> times(x,y) times(times(z,x),y) -> times(f(x),y) SUCCESS Search time: 0.17 seconds |
5.27
OutputCOMPLETE SYSTEM: *(g(x),y) -> *(x,y) *(g(x),x) -> *(x,x) *(x,g(x)) -> g(x) *(x,f(x)) -> *(x,x) g(g(x)) -> g(x) *(x,*(y,z)) -> *(x,g(y)) f(g(x)) -> g(x) g(*(x,x)) -> f(x) f(f(x)) -> f(x) g(f(x)) -> f(x) f(*(x,x)) -> g(x) *(f(x),x) -> f(x) *(x,f(y)) -> *(x,y) g(*(x,y)) -> f(y) f(*(x,y)) -> g(x) *(*(x,x),y) -> *(f(x),y) *(*(z,x),y) -> *(f(x),y) *(f(x),g(x)) -> x *(x,*(y,y)) -> *(x,g(y)) STATISTICS: General number of iterations: 96 number of nodes: 1731 number of processes: 12 time for orient: 2.20 time for rewrite: 0.31 time for deduce: 1.08 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.315118 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.05 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 371 (yes: 272, timeouts: 0) time limit for check: 2.00 termination time: 2.12 Deduction critical pair criterion: all redundant CPs in total: 2031 for successful process: 207 required time: 0.14 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.03 overlaps: 0.05 maintenance: 0.00 One: 0.016289 Two: 0.000000 COMPLETE SYSTEM: *(g(x),y) -> *(x,y) *(g(x),x) -> *(x,x) *(x,g(x)) -> g(x) *(x,f(x)) -> *(x,x) g(g(x)) -> g(x) *(x,*(y,z)) -> *(x,g(y)) f(g(x)) -> g(x) g(*(x,x)) -> f(x) f(f(x)) -> f(x) g(f(x)) -> f(x) f(*(x,x)) -> g(x) *(f(x),x) -> f(x) *(x,f(y)) -> *(x,y) g(*(x,y)) -> f(y) f(*(x,y)) -> g(x) *(*(x,x),y) -> *(f(x),y) *(*(z,x),y) -> *(f(x),y) *(f(x),g(x)) -> x *(x,*(y,y)) -> *(x,g(y)) |
8.84 |
SK90_3.06 |
3.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 9 equalities: 105 restarts: 0 time/cache: 0 time/set ops: 0.008 time/maxk: 2.645 time/normalization: 0.17 time/overlaps: 0.097 time/orientation constraints: 0.014 time/project: 0 time/sat: 0.088 time/update context: 0.092 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))) |
0.24
OutputEQUATIONS:
Completion of SK90_3.06
times(x,times(y,z)) = times(times(x,y),z) times(1(),1()) = 1() times(x,i(x)) = 1() g(times(x,y),y) = f(times(x,y),x) f(1(),y) = y COMPLETE TRS: RULES: g(1(),1()) -> 1() times(x,g(1(),x)) -> 1() g(1(),g(1(),x)) -> x times(g(1(),x),x) -> 1() times(1(),x) -> x f(x,y) -> g(x,times(g(1(),y),x)) g(1(),times(x,y)) -> times(g(1(),y),g(1(),x)) times(times(x,y),z) -> times(x,times(y,z)) i(x) -> g(1(),x) times(x,1()) -> x times(y,times(g(1(),y),x)) -> x times(g(1(),y),times(y,x)) -> x SUCCESS Search time: 0.24 seconds |
3.16
OutputCOMPLETE SYSTEM: *(x,*(y,z)) -> *(*(x,y),z) g(1(),1()) -> 1() *(x,1()) -> x *(1(),x) -> x f(x,x) -> g(x,1()) i(x) -> g(1(),x) g(1(),g(1(),x)) -> x *(x,g(1(),x)) -> 1() *(g(1(),x),x) -> 1() *(*(x,y),g(1(),y)) -> x *(*(x,g(1(),y)),y) -> x f(x,y) -> g(x,*(g(1(),y),x)) g(1(),*(x,y)) -> *(g(1(),y),g(1(),x)) STATISTICS: General number of iterations: 71 number of nodes: 1360 number of processes: 11 time for orient: 1.92 time for rewrite: 0.19 time for deduce: 0.23 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.03 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 306 (yes: 204, timeouts: 0) time limit for check: 2.00 termination time: 1.84 Deduction critical pair criterion: all redundant CPs in total: 686 for successful process: 26 required time: 0.02 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.01 overlaps: 0.01 maintenance: 0.00 One: 0.009241 Two: 0.000000 COMPLETE SYSTEM: *(x,*(y,z)) -> *(*(x,y),z) g(1(),1()) -> 1() *(x,1()) -> x *(1(),x) -> x f(x,x) -> g(x,1()) i(x) -> g(1(),x) g(1(),g(1(),x)) -> x *(x,g(1(),x)) -> 1() *(g(1(),x),x) -> 1() *(*(x,y),g(1(),y)) -> x *(*(x,g(1(),y)),y) -> x f(x,y) -> g(x,*(g(1(),y),x)) g(1(),*(x,y)) -> *(g(1(),y),g(1(),x)) |
9.73 |
SK90_3.07 |
5.61
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 10 equalities: 120 restarts: 0 time/cache: 0 time/set ops: 0.011 time/maxk: 5.023 time/normalization: 0.323 time/overlaps: 0.132 time/orientation constraints: 0.017 time/project: 0 time/sat: 0.076 time/update context: 0.183 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,) |
1.23
OutputEQUATIONS:
Completion of SK90_3.07
plus(plus(x,y),z) = plus(x,plus(y,z)) plus(0(),0()) = 0() plus(x,minus(x)) = 0() f(0(),y,z) = y g(plus(x,y),y) = f(plus(x,y),x,y) COMPLETE TRS: RULES: plus(plus(x,y),z) -> plus(x,plus(y,z)) plus(x,minus(x)) -> 0() f(0(),y,z) -> y minus(0()) -> 0() minus(minus(x)) -> x plus(minus(x),x) -> 0() plus(0(),x) -> x plus(minus(x),plus(x,y)) -> y plus(y,plus(minus(y),x)) -> x plus(x,0()) -> x minus(plus(y,x)) -> plus(minus(x),minus(y)) g(x,y) -> f(x,plus(x,minus(y)),y) SUCCESS Search time: 1.23 seconds |
⊥ | 9.80 |
SK90_3.08 |
0.02
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 12 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.005 time/normalization: 0.001 time/overlaps: 0.004 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,) |
0.00
OutputEQUATIONS:
Completion of SK90_3.08
times(x,\(x,y)) = y \(x,times(x,y)) = y slash(times(x,y),y) = x times(slash(x,y),y) = x times(x,times(y,x)) = y COMPLETE TRS: RULES: times(x,y) -> slash(y,x) \(x,y) -> slash(x,y) slash(slash(x,y),x) -> y slash(x,slash(y,x)) -> y SUCCESS Search time: 0.00 seconds |
0.02
OutputCOMPLETE SYSTEM: *(x,*(y,x)) -> y \(x,y) -> *(y,x) /(x,y) -> *(y,x) *(*(x,y),x) -> y STATISTICS: General number of iterations: 9 number of nodes: 21 number of processes: 2 time for orient: 0.01 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 10 (yes: 10, timeouts: 0) time limit for check: 2.00 termination time: 0.01 Deduction critical pair criterion: all redundant CPs in total: 7 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000132 Two: 0.000000 COMPLETE SYSTEM: *(x,*(y,x)) -> y \(x,y) -> *(y,x) /(x,y) -> *(y,x) *(*(x,y),x) -> y |
3.82 |
SK90_3.09 | ∞ | ⊥ | ⊥ | 203.10 |
SK90_3.10 |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 8 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.003 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)
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,) |
0.00
OutputEQUATIONS:
Completion of SK90_3.10
f(x,times(x,y)) = y g(times(x,y),y) = x times(x,one()) = x times(one(),y) = y COMPLETE TRS: RULES: f(x,times(x,y)) -> y g(times(x,y),y) -> x times(x,one()) -> x times(one(),y) -> y f(x,x) -> one() g(x,one()) -> x f(one(),x) -> x g(x,x) -> one() SUCCESS Search time: 0.00 seconds |
0.01
OutputCOMPLETE SYSTEM: *(x,one()) -> x *(one(),x) -> x f(x,*(x,y)) -> y f(one(),x) -> x f(x,x) -> one() g(*(x,y),y) -> x g(x,x) -> one() g(x,one()) -> x STATISTICS: General number of iterations: 9 number of nodes: 8 number of processes: 0 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 8 (yes: 8, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 4 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000098 Two: 0.000000 COMPLETE SYSTEM: *(x,one()) -> x *(one(),x) -> x f(x,*(x,y)) -> y f(one(),x) -> x f(x,x) -> one() g(*(x,y),y) -> x g(x,x) -> one() g(x,one()) -> x |
2.27 |
SK90_3.11 |
0.04
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 3 equalities: 12 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.025 time/normalization: 0 time/overlaps: 0.005 time/orientation constraints: 0.001 time/project: 0 time/sat: 0.001 time/update context: 0.001 Convergent TRS(VAR x)
Completion of SK90_3.11
(RULES p(x) → x,s(x) → x,+(x,0) → x,) |
0.00
OutputEQUATIONS:
Completion of SK90_3.11
p(0()) = 0() p(s(x)) = x plus(x,0()) = x s(plus(x,p(y))) = plus(x,y) COMPLETE TRS: RULES: plus(x,0()) -> x s(x) -> x p(x) -> x SUCCESS Search time: 0.00 seconds |
0.02
OutputCOMPLETE SYSTEM: +(x,0()) -> x s(x) -> x p(x) -> x STATISTICS: General number of iterations: 7 number of nodes: 13 number of processes: 0 time for orient: 0.02 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 7 (yes: 6, timeouts: 0) time limit for check: 2.00 termination time: 0.02 Deduction critical pair criterion: all redundant CPs in total: 3 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000095 Two: 0.000000 COMPLETE SYSTEM: +(x,0()) -> x s(x) -> x p(x) -> x |
2.01 |
SK90_3.12 | ∞ | ⊥ |
0.20
OutputCOMPLETE SYSTEM: /(x,x) -> 1() /(x,1()) -> x i(/(x,y)) -> /(y,x) i(1()) -> 1() /(1(),x) -> i(x) i(i(x)) -> x /(x,/(z,y)) -> /(/(x,i(y)),z) /(/(x,y),i(y)) -> x /(/(x,i(y)),y) -> x STATISTICS: General number of iterations: 15 number of nodes: 196 number of processes: 5 time for orient: 0.12 time for rewrite: 0.02 time for deduce: 0.04 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.002269 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 27 (yes: 24, timeouts: 0) time limit for check: 2.00 termination time: 0.12 Deduction critical pair criterion: all redundant CPs in total: 137 for successful process: 8 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000238 Two: 0.000000 COMPLETE SYSTEM: /(x,x) -> 1() /(x,1()) -> x i(/(x,y)) -> /(y,x) i(1()) -> 1() /(1(),x) -> i(x) i(i(x)) -> x /(x,/(z,y)) -> /(/(x,i(y)),z) /(/(x,y),i(y)) -> x /(/(x,i(y)),y) -> x |
⊥ |
SK90_3.13 |
0.03
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 15 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.019 time/normalization: 0.002 time/overlaps: 0.003 time/orientation constraints: 0 time/project: 0 time/sat: 0.012 time/update context: 0 Convergent TRS(VAR x y z)
Completion of SK90_3.13
(RULES 1 → exp(0)+(x,+(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))) |
0.02
OutputEQUATIONS:
Completion of SK90_3.13
plus(plus(x,y),z) = plus(x,plus(y,z)) plus(x,0()) = x times(times(x,y),z) = times(x,times(y,z)) times(x,1()) = x exp(0()) = 1() exp(plus(x,y)) = times(exp(x),exp(y)) COMPLETE TRS: RULES: plus(plus(x,y),z) -> plus(x,plus(y,z)) plus(x,0()) -> x times(times(x,y),z) -> times(x,times(y,z)) exp(plus(x,y)) -> times(exp(x),exp(y)) times(x,exp(0())) -> x 1() -> exp(0()) plus(x,plus(0(),y)) -> plus(x,y) times(x,times(exp(0()),y)) -> times(x,y) SUCCESS Search time: 0.02 seconds |
0.13
OutputCOMPLETE SYSTEM: exp(0()) -> 1() +(x,0()) -> x *(x,1()) -> x +(x,+(y,z)) -> +(+(x,y),z) *(x,*(y,z)) -> *(*(x,y),z) exp(+(x,y)) -> *(exp(x),exp(y)) STATISTICS: General number of iterations: 7 number of nodes: 34 number of processes: 15 time for orient: 0.10 time for rewrite: 0.00 time for deduce: 0.01 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 33 (yes: 33, timeouts: 0) time limit for check: 2.00 termination time: 0.10 Deduction critical pair criterion: all redundant CPs in total: 17 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000357 Two: 0.000000 COMPLETE SYSTEM: exp(0()) -> 1() +(x,0()) -> x *(x,1()) -> x +(x,+(y,z)) -> +(+(x,y),z) *(x,*(y,z)) -> *(*(x,y),z) exp(+(x,y)) -> *(exp(x),exp(y)) |
2.96 |
SK90_3.14 |
0.03
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 15 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.015 time/normalization: 0.001 time/overlaps: 0.004 time/orientation constraints: 0.001 time/project: 0 time/sat: 0.004 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)) |
0.01
OutputEQUATIONS:
Completion of SK90_3.14
s(s(x)) = x f(0(),y) = y f(s(x),y) = s(f(x,y)) f(f(g(x,y),0()),0()) = g(x,y) g(0(),y) = y g(s(x),y) = f(g(x,y),0()) h(0()) = s(0()) COMPLETE TRS: RULES: s(s(x)) -> x f(0(),y) -> y f(s(x),y) -> s(f(x,y)) g(0(),y) -> y g(s(x),y) -> f(g(x,y),0()) h(0()) -> s(0()) f(f(x,0()),0()) -> x SUCCESS Search time: 0.01 seconds |
0.13
OutputCOMPLETE SYSTEM: h(0()) -> s(0()) s(s(x)) -> x f(0(),x) -> x g(0(),x) -> x f(s(x),y) -> s(f(x,y)) f(g(x,y),0()) -> g(s(x),y) g(s(0()),x) -> f(x,0()) f(f(x,0()),0()) -> x STATISTICS: General number of iterations: 10 number of nodes: 41 number of processes: 9 time for orient: 0.09 time for rewrite: 0.01 time for deduce: 0.01 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 34 (yes: 34, timeouts: 0) time limit for check: 2.00 termination time: 0.09 Deduction critical pair criterion: all redundant CPs in total: 21 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000367 Two: 0.000000 COMPLETE SYSTEM: h(0()) -> s(0()) s(s(x)) -> x f(0(),x) -> x g(0(),x) -> x f(s(x),y) -> s(f(x,y)) f(g(x,y),0()) -> g(s(x),y) g(s(0()),x) -> f(x,0()) f(f(x,0()),0()) -> x |
2.79 |
SK90_3.15 |
0.45
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 14 equalities: 10 restarts: 1 time/cache: 0 time/set ops: 0 time/maxk: 0.295 time/normalization: 0.06 time/overlaps: 0.039 time/orientation constraints: 0.015 time/project: 0 time/sat: 0.005 time/update context: 0.011 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)) |
⊥ |
0.06
OutputCOMPLETE SYSTEM: p(s(x)) -> x eq(x,x) -> true() eq(s(x),x) -> false() eq(x,s(x)) -> false() eq(x,p(x)) -> false() eq(p(x),x) -> false() eq(p(x),p(y)) -> eq(x,y) eq(x,s(y)) -> eq(p(x),y) eq(s(x),y) -> eq(x,p(y)) STATISTICS: General number of iterations: 11 number of nodes: 26 number of processes: 3 time for orient: 0.04 time for rewrite: 0.00 time for deduce: 0.01 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.000208 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 16 (yes: 14, timeouts: 0) time limit for check: 2.00 termination time: 0.03 Deduction critical pair criterion: all redundant CPs in total: 16 for successful process: 2 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000176 Two: 0.000000 COMPLETE SYSTEM: p(s(x)) -> x eq(x,x) -> true() eq(s(x),x) -> false() eq(x,s(x)) -> false() eq(x,p(x)) -> false() eq(p(x),x) -> false() eq(p(x),p(y)) -> eq(x,y) eq(x,s(y)) -> eq(p(x),y) eq(s(x),y) -> eq(x,p(y)) |
∞ |
SK90_3.16 |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 5 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_3.16
(RULES atom(x) → falsecar(.(x,y)) → x,cdr(.(x,y)) → y,.(car(x),cdr(x)) → x,) |
0.00
OutputEQUATIONS:
Completion of SK90_3.16
car(cons(x,y)) = x cdr(cons(x,y)) = y cons(car(x),cdr(x)) = x atom(cons(x,y)) = false_() COMPLETE TRS: RULES: car(cons(x,y)) -> x cdr(cons(x,y)) -> y cons(car(x),cdr(x)) -> x atom(x) -> false_() SUCCESS Search time: 0.00 seconds |
0.01
OutputCOMPLETE SYSTEM: car(.(x,y)) -> x cdr(.(x,y)) -> y .(car(x),cdr(x)) -> x atom(x) -> false() STATISTICS: General number of iterations: 6 number of nodes: 6 number of processes: 0 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 5 (yes: 5, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 3 for successful process: 1 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000088 Two: 0.000000 COMPLETE SYSTEM: car(.(x,y)) -> x cdr(.(x,y)) -> y .(car(x),cdr(x)) -> x atom(x) -> false() |
2.79 |
SK90_3.17 |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 6 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.002 time/normalization: 0.001 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,) |
0.00
OutputEQUATIONS:
Completion of SK90_3.17
or_(&(x,y),&(z,y)) = &(or_(x,z),y) &(x,x) = x or_(x,x) = x COMPLETE TRS: RULES: or_(&(x,y),&(z,y)) -> &(or_(x,z),y) &(x,x) -> x or_(x,x) -> x or_(x,&(y,x)) -> &(or_(x,y),x) or_(&(x,y),y) -> &(or_(x,y),y) SUCCESS Search time: 0.00 seconds |
0.06
OutputCOMPLETE SYSTEM: &(x,x) -> x or(x,x) -> x or(&(x,z),&(y,z)) -> &(or(x,y),z) or(&(x,y),y) -> &(or(x,y),y) or(x,&(y,x)) -> &(or(x,y),x) STATISTICS: General number of iterations: 6 number of nodes: 24 number of processes: 4 time for orient: 0.04 time for rewrite: 0.00 time for deduce: 0.01 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 10 (yes: 10, timeouts: 0) time limit for check: 2.00 termination time: 0.04 Deduction critical pair criterion: all redundant CPs in total: 20 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000103 Two: 0.000000 COMPLETE SYSTEM: &(x,x) -> x or(x,x) -> x or(&(x,z),&(y,z)) -> &(or(x,y),z) or(&(x,y),y) -> &(or(x,y),y) or(x,&(y,x)) -> &(or(x,y),x) |
3.18 |
SK90_3.18 |
0.06
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 3 equalities: 15 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.037 time/normalization: 0.004 time/overlaps: 0.007 time/orientation constraints: 0.006 time/project: 0 time/sat: 0.001 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,) |
0.01
OutputEQUATIONS:
Completion of SK90_3.18
app(nil(),y) = y app(cons(x,y),z) = cons(x,app(y,z)) rev(nil()) = nil() rev(cons(x,y)) = app(rev(y),cons(x,nil())) rev(rev(x)) = x COMPLETE TRS: RULES: app(nil(),y) -> y app(cons(x,y),z) -> cons(x,app(y,z)) rev(nil()) -> nil() rev(cons(x,y)) -> app(rev(y),cons(x,nil())) rev(rev(x)) -> x rev(app(x,cons(y,nil()))) -> cons(y,rev(x)) SUCCESS Search time: 0.01 seconds |
0.20
OutputCOMPLETE SYSTEM: rev(nil()) -> nil() @(nil(),y) -> y rev(rev(y)) -> y @(.(y,x),z) -> .(y,@(x,z)) rev(.(y,x)) -> @(rev(x),.(y,nil())) rev(@(y,.(x,nil()))) -> .(x,rev(y)) STATISTICS: General number of iterations: 12 number of nodes: 78 number of processes: 10 time for orient: 0.14 time for rewrite: 0.01 time for deduce: 0.02 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 35 (yes: 30, timeouts: 0) time limit for check: 2.00 termination time: 0.14 Deduction critical pair criterion: all redundant CPs in total: 43 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000195 Two: 0.000000 COMPLETE SYSTEM: rev(nil()) -> nil() @(nil(),y) -> y rev(rev(y)) -> y @(.(y,x),z) -> .(y,@(x,z)) rev(.(y,x)) -> @(rev(x),.(y,nil())) rev(@(y,.(x,nil()))) -> .(x,rev(y)) |
3.25 |
SK90_3.19 |
0.06
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 23 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.031 time/normalization: 0.009 time/overlaps: 0.005 time/orientation constraints: 0.004 time/project: 0 time/sat: 0.002 time/update context: 0.002 Convergent TRS(VAR y x z)
Completion of SK90_3.19
(RULES @(.(y,x),z) → .(y,@(x,z))@(reviter(y,x),z) → reviter(y,@(x,z))@(nil,y) → y,@(@(y,x),z) → @(y,@(x,z))reviter(nil,y) → y,reviter(.(y,x),z) → reviter(x,.(y,z))rev(y) → reviter(y,nil)) |
0.04
OutputEQUATIONS:
Completion of SK90_3.19
app(nil(),y) = y app(cons(x,y),z) = cons(x,app(y,z)) app(app(x,y),z) = app(x,app(y,z)) reviter(nil(),y) = y reviter(cons(x,y),z) = reviter(y,cons(x,z)) rev(nil()) = nil() rev(cons(x,y)) = app(rev(y),cons(x,nil())) app(rev(x),y) = reviter(x,y) rev(x) = reviter(x,nil()) COMPLETE TRS: RULES: app(nil(),y) -> y app(cons(x,y),z) -> cons(x,app(y,z)) app(app(x,y),z) -> app(x,app(y,z)) reviter(nil(),y) -> y reviter(cons(x,y),z) -> reviter(y,cons(x,z)) rev(x) -> reviter(x,nil()) app(reviter(x,y),z) -> reviter(x,app(y,z)) SUCCESS Search time: 0.04 seconds |
0.46
OutputCOMPLETE SYSTEM: @(nil(),y) -> y reviter(nil(),y) -> y rev(y) -> reviter(y,nil()) @(.(y,x),z) -> .(y,@(x,z)) @(@(y,x),z) -> @(y,@(x,z)) reviter(.(y,x),z) -> reviter(x,.(y,z)) @(reviter(y,x),z) -> reviter(y,@(x,z)) STATISTICS: General number of iterations: 11 number of nodes: 80 number of processes: 35 time for orient: 0.40 time for rewrite: 0.01 time for deduce: 0.03 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 89 (yes: 81, timeouts: 0) time limit for check: 2.00 termination time: 0.39 Deduction critical pair criterion: all redundant CPs in total: 41 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000400 Two: 0.000000 COMPLETE SYSTEM: @(nil(),y) -> y reviter(nil(),y) -> y rev(y) -> reviter(y,nil()) @(.(y,x),z) -> .(y,@(x,z)) @(@(y,x),z) -> @(y,@(x,z)) reviter(.(y,x),z) -> reviter(x,.(y,z)) @(reviter(y,x),z) -> reviter(y,@(x,z)) |
3.40 |
SK90_3.20 |
0.10
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 30 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.034 time/normalization: 0.004 time/overlaps: 0.024 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.003 time/update context: 0.006 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) |
0.53
OutputEQUATIONS:
Completion of SK90_3.20
eq(x,x) = true_() eq(nil(),end(y,z)) = false_() eq(end(x,y),nil()) = false_() eq(end(x,y),end(u,v)) = and_(eq(y,v),eq(x,u)) f(x,nil()) = end(nil(),x) f(x,end(y,z)) = end(f(x,y),z) cons(nil(),y) = y cons(end(x,y),z) = cons(x,f(y,z)) null(nil()) = true_() null(end(x,y)) = false_() COMPLETE TRS: RULES: eq(x,x) -> null(nil()) eq(nil(),end(y,z)) -> false_() eq(end(x,y),nil()) -> false_() eq(end(x,y),end(u,v)) -> and_(eq(y,v),eq(x,u)) f(x,nil()) -> end(nil(),x) f(x,end(y,z)) -> end(f(x,y),z) cons(nil(),y) -> y cons(end(x,y),z) -> cons(x,f(y,z)) null(end(x,y)) -> false_() and_(null(nil()),null(nil())) -> null(nil()) true_() -> null(nil()) SUCCESS Search time: 0.53 seconds |
0.32
OutputCOMPLETE SYSTEM: null(nil()) -> true() f(x,nil()) -> end(nil(),x) .(nil(),x) -> x eq(x,x) -> true() null(end(x,y)) -> false() eq(nil(),end(x,y)) -> false() eq(end(x,y),nil()) -> false() f(x,end(y,z)) -> end(f(x,y),z) .(end(x,y),z) -> .(x,f(y,z)) eq(end(z,x),end(u,y)) -> and(eq(x,y),eq(z,u)) and(true(),true()) -> true() STATISTICS: General number of iterations: 13 number of nodes: 46 number of processes: 31 time for orient: 0.26 time for rewrite: 0.01 time for deduce: 0.02 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 90 (yes: 90, timeouts: 0) time limit for check: 2.00 termination time: 0.25 Deduction critical pair criterion: all redundant CPs in total: 27 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000837 Two: 0.000000 COMPLETE SYSTEM: null(nil()) -> true() f(x,nil()) -> end(nil(),x) .(nil(),x) -> x eq(x,x) -> true() null(end(x,y)) -> false() eq(nil(),end(x,y)) -> false() eq(end(x,y),nil()) -> false() f(x,end(y,z)) -> end(f(x,y),z) .(end(x,y),z) -> .(x,f(y,z)) eq(end(z,x),end(u,y)) -> and(eq(x,y),eq(z,u)) and(true(),true()) -> true() |
3.43 |
SK90_3.21 |
0.45
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 3 equalities: 78 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 0.313 time/normalization: 0.059 time/overlaps: 0.04 time/orientation constraints: 0.009 time/project: 0 time/sat: 0.003 time/update context: 0.023 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) |
0.01
OutputEQUATIONS:
Completion of SK90_3.21
f(x,nil()) = g(nil(),x) f(x,g(y,z)) = g(f(x,y),z) g(g(x,y),y) = g(x,y) g(cdr(g(x,y)),y) = cdr(g(x,y)) cons(x,nil()) = x cons(x,g(y,z)) = g(cons(x,y),z) cdr(nil()) = nil() cdr(g(nil(),y)) = nil() cdr(g(g(x,y),z)) = g(cdr(g(x,y)),z) COMPLETE TRS: RULES: cons(x,nil()) -> x cdr(nil()) -> nil() f(x,nil()) -> nil() g(x,y) -> x SUCCESS Search time: 0.01 seconds |
0.16
OutputCOMPLETE SYSTEM: cdr(nil()) -> nil() cons(x,nil()) -> x g(x,y) -> x f(x,nil()) -> nil() STATISTICS: General number of iterations: 13 number of nodes: 76 number of processes: 7 time for orient: 0.12 time for rewrite: 0.01 time for deduce: 0.01 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 43 (yes: 43, timeouts: 0) time limit for check: 2.00 termination time: 0.11 Deduction critical pair criterion: all redundant CPs in total: 23 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000343 Two: 0.000000 COMPLETE SYSTEM: cdr(nil()) -> nil() cons(x,nil()) -> x g(x,y) -> x f(x,nil()) -> nil() |
3.05 |
SK90_3.22 |
41.77
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 15 equalities: 274 restarts: 0 time/cache: 0 time/set ops: 0.078 time/maxk: 40.41 time/normalization: 1.116 time/overlaps: 0.05 time/orientation constraints: 0.172 time/project: 0 time/sat: 0.411 time/update context: 1.573 Convergent TRS(VAR x)
Completion of SK90_3.22
(RULES c(x) → d(d(d(d(x))))d(d(d(d(d(d(d(d(d(d(d(d(x)))))))))))) → d(x)e(x) → d(d(d(x)))b(x) → d(d(d(d(d(x)))))a(x) → d(d(d(d(d(d(d(d(d(x)))))))))) |
0.71
OutputEQUATIONS:
Completion of SK90_3.22
a(e(x)) = d(x) b(a(x)) = e(x) a(x) = c(b(x)) b(x) = d(c(x)) c(x) = e(d(x)) COMPLETE TRS: RULES: a(x) -> b(b(b(b(x)))) c(x) -> b(b(b(x))) d(x) -> b(b(b(b(b(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) SUCCESS Search time: 0.71 seconds |
⊥ | 7.53 |
SK90_3.23 |
0.27
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 5 equalities: 57 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.241 time/normalization: 0.008 time/overlaps: 0.011 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.005 time/update context: 0.013 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))) |
8.47
OutputEQUATIONS:
Completion of SK90_3.23
b(d(x)) = x d(a(x)) = e(x) e(c(x)) = a(x) c(e(x)) = a(x) COMPLETE TRS: RULES: b(d(x)) -> x c(a(x)) -> a(c(x)) b(a(x)) -> a(c(x)) c(d(a(x))) -> a(x) e(x) -> d(a(x)) d(a(a(x))) -> a(d(a(x))) d(a(c(x))) -> a(x) SUCCESS Search time: 8.47 seconds |
0.26
OutputCOMPLETE SYSTEM: b(d(x)) -> x d(a(x)) -> e(x) e(c(x)) -> a(x) c(e(x)) -> a(x) c(a(x)) -> a(c(x)) b(e(x)) -> a(x) b(a(x)) -> a(c(x)) e(a(x)) -> a(e(x)) STATISTICS: General number of iterations: 19 number of nodes: 70 number of processes: 16 time for orient: 0.18 time for rewrite: 0.02 time for deduce: 0.01 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.005229 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 48 (yes: 45, timeouts: 0) time limit for check: 2.00 termination time: 0.18 Deduction critical pair criterion: all redundant CPs in total: 35 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000571 Two: 0.000000 COMPLETE SYSTEM: b(d(x)) -> x d(a(x)) -> e(x) e(c(x)) -> a(x) c(e(x)) -> a(x) c(a(x)) -> a(c(x)) b(e(x)) -> a(x) b(a(x)) -> a(c(x)) e(a(x)) -> a(e(x)) |
∞ |
SK90_3.24 |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 8 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.007 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)) |
0.00
OutputEQUATIONS:
Completion of SK90_3.24
a(b(a(x))) = b(a(x)) c(x) = a(x) c(x) = b(x) COMPLETE TRS: RULES: c(x) -> b(x) a(x) -> b(x) b(b(b(x))) -> b(b(x)) SUCCESS Search time: 0.00 seconds |
0.02
OutputCOMPLETE SYSTEM: c(x) -> b(x) a(x) -> b(x) b(b(b(x))) -> b(b(x)) STATISTICS: General number of iterations: 5 number of nodes: 16 number of processes: 3 time for orient: 0.01 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.000074 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 8 (yes: 8, timeouts: 0) time limit for check: 2.00 termination time: 0.01 Deduction critical pair criterion: all redundant CPs in total: 0 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.002464 Two: 0.000000 COMPLETE SYSTEM: c(x) -> b(x) a(x) -> b(x) b(b(b(x))) -> b(b(x)) |
3.94 |
SK90_3.25 |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 2 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_3.25
(RULES a(a(a(b(x)))) → a(b(a(a(x))))a(b(a(a(b(x))))) → a(x)) |
0.18
OutputEQUATIONS:
Completion of SK90_3.25
a(b(a(a(b(x))))) = a(x) COMPLETE TRS: RULES: a(b(a(a(b(x))))) -> a(x) a(a(a(b(x)))) -> a(b(a(a(x)))) SUCCESS Search time: 0.18 seconds |
0.02
OutputCOMPLETE SYSTEM: a(b(a(a(b(x))))) -> a(x) a(a(a(b(x)))) -> a(b(a(a(x)))) STATISTICS: General number of iterations: 3 number of nodes: 8 number of processes: 1 time for orient: 0.01 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.000024 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 4 (yes: 3, timeouts: 0) time limit for check: 2.00 termination time: 0.01 Deduction critical pair criterion: all redundant CPs in total: 3 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000048 Two: 0.000000 COMPLETE SYSTEM: a(b(a(a(b(x))))) -> a(x) a(a(a(b(x)))) -> a(b(a(a(x)))) |
4.03 |
SK90_3.26 | ∞ |
22.09
OutputEQUATIONS:
Completion of SK90_3.26
a(c(x)) = c(b(b(x))) b(a(x)) = a(c(c(x))) c(b(x)) = b(a(a(x))) u(a(x)) = x v(b(x)) = x w(c(x)) = x COMPLETE TRS: RULES: w(w(w(w(w(w(w(x))))))) -> x u(w(w(w(u(x))))) -> w(w(w(w(x)))) u(w(u(x))) -> w(w(w(w(u(w(x)))))) u(w(w(w(w(w(w(u(x)))))))) -> w(u(w(w(x)))) u(w(w(w(w(u(x)))))) -> w(w(w(u(w(w(w(w(w(x))))))))) u(w(w(w(w(w(u(x))))))) -> w(w(w(w(w(w(u(w(w(w(x)))))))))) a(x) -> w(w(w(u(w(w(w(x))))))) b(x) -> u(w(x)) v(x) -> w(w(u(w(w(w(x)))))) c(x) -> w(w(w(w(w(w(x)))))) u(w(w(u(x)))) -> w(w(u(w(w(w(w(x))))))) u(u(x)) -> w(w(w(w(w(u(w(w(w(w(w(w(x)))))))))))) SUCCESS Search time: 22.09 seconds |
⊥ | 187.18 |
SK90_3.27 |
6.22
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 6 equalities: 110 restarts: 0 time/cache: 0 time/set ops: 0.036 time/maxk: 5.743 time/normalization: 0.337 time/overlaps: 0.034 time/orientation constraints: 0.059 time/project: 0 time/sat: 0.042 time/update context: 0.43 Convergent TRS(VAR x)
Completion of SK90_3.27
(RULES c(x) → x,a(x) → x,b(x) → x,) |
6.94
OutputEQUATIONS:
Completion of SK90_3.27
a(x) = c(c(c(b(c(c(x)))))) b(c(b(x))) = c(c(b(c(x)))) b(c(c(b(x)))) = c(c(c(c(c(c(b(c(c(c(c(c(x)))))))))))) b(c(c(c(b(x))))) = c(b(c(c(c(c(x)))))) b(b(c(c(c(b(x)))))) = c(c(c(c(b(c(c(x))))))) b(c(c(c(c(c(b(x))))))) = c(c(x)) b(c(c(c(c(c(c(b(x)))))))) = c(c(c(c(c(b(c(c(c(x))))))))) c(c(c(c(c(c(c(x))))))) = x COMPLETE TRS: RULES: c(x) -> x b(x) -> x a(x) -> x SUCCESS Search time: 6.94 seconds |
4.21
OutputCOMPLETE SYSTEM: c(x) -> x b(x) -> x a(x) -> x STATISTICS: General number of iterations: 40 number of nodes: 2724 number of processes: 4 time for orient: 2.11 time for rewrite: 0.55 time for deduce: 0.19 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.125223 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.04 Process Killing killed 18 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 155 (yes: 107, timeouts: 0) time limit for check: 2.00 termination time: 1.95 Deduction critical pair criterion: all redundant CPs in total: 481 for successful process: 2 required time: 0.02 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.01 overlaps: 0.01 maintenance: 0.00 One: 0.007993 Two: 0.000000 COMPLETE SYSTEM: c(x) -> x b(x) -> x a(x) -> x |
7.85 |
SK90_3.28 |
47.89
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 15 equalities: 259 restarts: 0 time/cache: 0 time/set ops: 0.036 time/maxk: 47.153 time/normalization: 0.403 time/overlaps: 0.091 time/orientation constraints: 0.108 time/project: 0 time/sat: 3.332 time/update context: 1.142 Convergent TRS(VAR x)
Completion of SK90_3.28
(RULES a(w(x)) → c(a(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)))))))u(x) → c(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,) |
∞ |
40.93
OutputCOMPLETE SYSTEM: a(b(x)) -> b(u(x)) a(u(x)) -> x a(w(x)) -> c(a(x)) b(c(x)) -> c(v(x)) b(v(x)) -> x c(w(x)) -> x u(a(x)) -> x v(b(x)) -> x w(c(x)) -> x u(v(x)) -> v(a(x)) u(b(x)) -> b(a(x)) v(c(x)) -> c(b(x)) v(w(x)) -> w(b(x)) b(w(x)) -> w(v(x)) a(v(x)) -> v(u(x)) u(w(x)) -> c(u(x)) u(c(x)) -> w(u(x)) a(c(x)) -> w(a(x)) STATISTICS: General number of iterations: 42 number of nodes: 1501 number of processes: 122 time for orient: 29.95 time for rewrite: 0.83 time for deduce: 1.84 Isomorphism Check: renamings+ (detected automatically) time for checking: 3.444461 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.08 Process Killing killed 263 exceeding best by: 71% required time: 0.01 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 2410 (yes: 1599, timeouts: 0) time limit for check: 2.00 termination time: 28.16 Deduction critical pair criterion: all redundant CPs in total: 460 for successful process: 0 required time: 0.06 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.01 overlaps: 0.01 maintenance: 0.00 One: 0.056594 Two: 0.000000 COMPLETE SYSTEM: a(b(x)) -> b(u(x)) a(u(x)) -> x a(w(x)) -> c(a(x)) b(c(x)) -> c(v(x)) b(v(x)) -> x c(w(x)) -> x u(a(x)) -> x v(b(x)) -> x w(c(x)) -> x u(v(x)) -> v(a(x)) u(b(x)) -> b(a(x)) v(c(x)) -> c(b(x)) v(w(x)) -> w(b(x)) b(w(x)) -> w(v(x)) a(v(x)) -> v(u(x)) u(w(x)) -> c(u(x)) u(c(x)) -> w(u(x)) a(c(x)) -> w(a(x)) |
∞ |
SK90_3.29 |
0.07
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 3 equalities: 37 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.053 time/normalization: 0.004 time/overlaps: 0.006 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.003 time/update context: 0.002 Convergent TRS(VAR x)
Completion of SK90_3.29
(RULES a(d(x)) → v(a(x))a(c(x)) → e(a(x))e(a(w(x))) → e(b(w(x)))v(b(w(x))) → e(b(w(x)))v(a(w(x))) → e(b(w(x)))d(w(x)) → c(w(x))b(c(x)) → e(b(x))b(d(x)) → v(b(x))u(x) → c(w(x))) |
1.17
OutputEQUATIONS:
Completion of SK90_3.29
a(c(x)) = e(a(x)) a(d(x)) = v(a(x)) b(c(x)) = e(b(x)) b(d(x)) = v(b(x)) a(u(x)) = b(u(x)) u(x) = c(w(x)) d(w(x)) = u(x) COMPLETE TRS: RULES: a(c(x)) -> e(a(x)) a(d(x)) -> v(a(x)) e(a(w(x))) -> b(d(w(x))) v(a(w(x))) -> b(d(w(x))) e(b(x)) -> b(c(x)) v(b(x)) -> b(d(x)) c(w(x)) -> d(w(x)) u(x) -> d(w(x)) SUCCESS Search time: 1.17 seconds |
1.18
OutputCOMPLETE SYSTEM: a(c(x)) -> e(a(x)) a(d(x)) -> v(a(x)) e(b(x)) -> b(c(x)) v(b(x)) -> b(d(x)) u(x) -> d(w(x)) c(w(x)) -> d(w(x)) e(a(w(x))) -> b(d(w(x))) v(a(w(x))) -> b(d(w(x))) STATISTICS: General number of iterations: 14 number of nodes: 100 number of processes: 92 time for orient: 0.85 time for rewrite: 0.03 time for deduce: 0.03 Isomorphism Check: renamings+ (detected automatically) time for checking: 0.109700 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 1 exceeding best by: 71% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 258 (yes: 256, timeouts: 0) time limit for check: 2.00 termination time: 0.81 Deduction critical pair criterion: all redundant CPs in total: 24 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.002589 Two: 0.000000 COMPLETE SYSTEM: a(c(x)) -> e(a(x)) a(d(x)) -> v(a(x)) e(b(x)) -> b(c(x)) v(b(x)) -> b(d(x)) u(x) -> d(w(x)) c(w(x)) -> d(w(x)) e(a(w(x))) -> b(d(w(x))) v(a(w(x))) -> b(d(w(x))) |
3.90 |
SK90_3.30 |
0.02
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 3 equalities: 13 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.013 time/normalization: 0 time/overlaps: 0 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) |
0.00
OutputEQUATIONS:
Completion of SK90_3.30
f(g(x),x) = a() f(g(x),y) = h(y) f(g(x),f(y,z)) = k(f(g(x),y),f(g(x),z)) COMPLETE TRS: RULES: f(g(x),y) -> a() h(x) -> a() k(a(),a()) -> a() SUCCESS Search time: 0.00 seconds |
0.01
OutputCOMPLETE SYSTEM: f(g(x),x) -> a() h(x) -> a() k(a(),a()) -> a() f(g(x),y) -> a() STATISTICS: General number of iterations: 6 number of nodes: 11 number of processes: 0 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 4 (yes: 4, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 1 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000073 Two: 0.000000 COMPLETE SYSTEM: f(g(x),x) -> a() h(x) -> a() k(a(),a()) -> a() f(g(x),y) -> a() |
2.73 |
SK90_3.31 |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 3 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))) |
0.00
OutputEQUATIONS:
Completion of SK90_3.31
f(x,h(y)) = j(x) f(h(x),y) = j(h(x)) g(f(x,x)) = i(x) COMPLETE TRS: RULES: f(x,h(y)) -> j(x) f(h(x),y) -> j(h(x)) g(f(x,x)) -> i(x) i(h(x)) -> g(j(h(x))) SUCCESS Search time: 0.00 seconds |
0.01
OutputCOMPLETE SYSTEM: f(x,h(y)) -> j(x) f(h(x),y) -> j(h(x)) i(x) -> g(f(x,x)) STATISTICS: General number of iterations: 4 number of nodes: 4 number of processes: 1 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 4 (yes: 4, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 1 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000085 Two: 0.000000 COMPLETE SYSTEM: f(x,h(y)) -> j(x) f(h(x),y) -> j(h(x)) i(x) -> g(f(x,x)) |
2.63 |
SK90_3.32 |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 4 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,) |
0.00
OutputEQUATIONS:
Completion of SK90_3.32
f(x,x) = x f(g(x),y) = g(x) g(g(x)) = x COMPLETE TRS: RULES: g(g(x)) -> x f(x,y) -> x SUCCESS Search time: 0.00 seconds |
0.01
OutputCOMPLETE SYSTEM: f(x,x) -> x g(g(x)) -> x f(x,y) -> x STATISTICS: General number of iterations: 5 number of nodes: 5 number of processes: 0 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.000021 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 4 (yes: 4, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 1 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.002910 Two: 0.000000 COMPLETE SYSTEM: f(x,x) -> x g(g(x)) -> x f(x,y) -> x |
2.62 |
SK90_3.33 |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 5 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 SK90_3.33
(RULES g(a) → af(x) → x,g(g(x)) → x,) |
0.00
OutputEQUATIONS:
Completion of SK90_3.33
f(g(x)) = g(x) g(a()) = a() g(g(x)) = x COMPLETE TRS: RULES: g(a()) -> a() g(g(x)) -> x f(x) -> x SUCCESS Search time: 0.00 seconds |
0.01
OutputCOMPLETE SYSTEM: g(a()) -> a() g(g(x)) -> x f(x) -> x STATISTICS: General number of iterations: 6 number of nodes: 7 number of processes: 0 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.000037 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 5 (yes: 5, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 2 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.002683 Two: 0.000000 COMPLETE SYSTEM: g(a()) -> a() g(g(x)) -> x f(x) -> x |
2.73 |
Sim91_sims2 | ∞ | ⊥ | ⊥ | ∞ |
TPDB_secret2006_torpa_secr10 |
8.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 9 equalities: 123 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 7.565 time/normalization: 0.27 time/overlaps: 0.076 time/orientation constraints: 0.041 time/project: 0 time/sat: 0.103 time/update context: 0.171 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)))c(c(a(x))) → c(c(c(x)))a(b(c(c(x)))) → c(c(x))a(c(b(x))) → c(b(c(b(x))))c(c(b(c(b(x))))) → c(b(c(b(x))))b(c(a(c(x)))) → b(c(c(c(x))))a(c(a(x))) → c(c(c(x)))c(b(c(b(c(b(x)))))) → c(b(c(b(x))))c(b(c(c(x)))) → c(c(c(x)))a(c(c(x))) → c(c(c(x)))c(c(c(b(x)))) → c(b(c(b(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)) |
0.18
OutputEQUATIONS:
Completion of TPDB_secret2006_torpa_secr10
a(a(x)) = c(b(a(b(a(x))))) b(a(b(x))) = b(x) a(a(a(x))) = c(c(a(x))) c(c(x)) = a(b(c(b(a(x))))) a(c(a(x))) = c(c(a(x))) c(a(c(x))) = a(a(c(x))) COMPLETE TRS: RULES: b(a(b(x))) -> b(x) a(c(a(x))) -> c(c(c(x))) a(a(x)) -> c(b(a(x))) a(b(c(b(x)))) -> c(c(b(x))) c(c(b(a(x)))) -> c(c(x)) a(c(b(x))) -> c(c(c(b(x)))) c(b(c(c(x)))) -> c(c(c(x))) c(c(a(x))) -> c(c(c(x))) a(c(c(x))) -> c(c(c(x))) b(c(a(c(x)))) -> b(c(c(c(x)))) b(c(b(a(x)))) -> b(c(c(x))) a(b(c(c(x)))) -> c(c(x)) c(b(a(c(x)))) -> c(a(c(x))) b(c(c(b(x)))) -> b(c(b(x))) c(c(c(c(x)))) -> c(c(c(x))) c(b(c(b(x)))) -> c(c(c(b(x)))) SUCCESS Search time: 0.18 seconds |
18.16
OutputCOMPLETE SYSTEM: b(a(b(x))) -> b(x) a(a(x)) -> c(b(a(x))) c(a(c(x))) -> c(b(a(c(x)))) a(b(c(b(x)))) -> c(c(b(x))) a(c(b(x))) -> c(b(c(b(x)))) b(c(c(b(x)))) -> b(c(b(x))) c(c(b(a(x)))) -> c(c(x)) b(c(b(a(x)))) -> b(c(c(x))) a(b(c(c(x)))) -> c(c(x)) c(b(c(c(x)))) -> c(c(c(x))) c(c(c(c(x)))) -> c(c(c(x))) c(c(c(b(x)))) -> c(b(c(b(x)))) c(c(b(c(b(x))))) -> c(b(c(b(x)))) c(b(c(b(c(b(x)))))) -> c(b(c(b(x)))) c(c(a(x))) -> c(c(c(x))) a(c(c(x))) -> c(c(c(x))) a(c(a(x))) -> c(c(c(x))) STATISTICS: General number of iterations: 169 number of nodes: 4929 number of processes: 20 time for orient: 8.90 time for rewrite: 1.96 time for deduce: 1.66 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.953524 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.08 Process Killing killed 1 exceeding best by: 401% required time: 0.01 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 573 (yes: 325, timeouts: 0) time limit for check: 2.00 termination time: 8.24 Deduction critical pair criterion: all redundant CPs in total: 3368 for successful process: 61 required time: 0.23 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.02 encompassments: 0.04 overlaps: 0.06 maintenance: 0.00 One: 0.016572 Two: 0.000000 COMPLETE SYSTEM: b(a(b(x))) -> b(x) a(a(x)) -> c(b(a(x))) c(a(c(x))) -> c(b(a(c(x)))) a(b(c(b(x)))) -> c(c(b(x))) a(c(b(x))) -> c(b(c(b(x)))) b(c(c(b(x)))) -> b(c(b(x))) c(c(b(a(x)))) -> c(c(x)) b(c(b(a(x)))) -> b(c(c(x))) a(b(c(c(x)))) -> c(c(x)) c(b(c(c(x)))) -> c(c(c(x))) c(c(c(c(x)))) -> c(c(c(x))) c(c(c(b(x)))) -> c(b(c(b(x)))) c(c(b(c(b(x))))) -> c(b(c(b(x)))) c(b(c(b(c(b(x)))))) -> c(b(c(b(x)))) c(c(a(x))) -> c(c(c(x))) a(c(c(x))) -> c(c(c(x))) a(c(a(x))) -> c(c(c(x))) |
7.51 |
TPDB_secret2006_torpa_secr4 |
1.82
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 5 equalities: 108 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 1.676 time/normalization: 0.081 time/overlaps: 0.027 time/orientation constraints: 0.042 time/project: 0 time/sat: 0.028 time/update context: 0.059 Convergent TRS(VAR x)
Completion of TPDB_secret2006_torpa_secr4
(RULES b(x) → d(d(x))a(x) → d(d(d(d(x))))c(d(x)) → d(d(d(d(x))))e(d(x)) → d(d(d(d(e(x)))))e(c(x)) → d(d(d(d(e(x)))))d(d(d(d(d(x))))) → d(d(d(d(x))))c(c(x)) → d(d(d(x)))d(d(d(c(x)))) → d(d(d(d(x))))) |
0.20
OutputEQUATIONS:
Completion of TPDB_secret2006_torpa_secr4
a(a(x)) = b(b(b(x))) a(x) = c(d(x)) b(b(x)) = c(c(c(x))) c(c(x)) = d(d(d(x))) e(d(x)) = a(b(c(d(e(x))))) b(x) = d(d(x)) e(c(x)) = b(a(a(e(x)))) c(d(d(x))) = a(x) COMPLETE TRS: RULES: a(x) -> c(c(c(x))) b(b(x)) -> c(c(c(x))) d(c(c(x))) -> c(c(c(x))) e(c(x)) -> c(c(c(e(x)))) e(b(x)) -> c(c(c(e(x)))) e(d(x)) -> c(c(c(e(x)))) d(b(x)) -> c(c(x)) c(b(x)) -> c(c(c(x))) d(d(x)) -> b(x) c(d(x)) -> c(c(c(x))) c(c(c(c(x)))) -> c(c(c(x))) b(d(x)) -> c(c(x)) b(c(c(x))) -> c(c(c(x))) SUCCESS Search time: 0.20 seconds |
3.67
OutputCOMPLETE SYSTEM: c(d(x)) -> a(x) b(x) -> d(d(x)) a(d(x)) -> a(x) d(d(d(x))) -> c(c(x)) c(c(c(x))) -> a(x) c(a(x)) -> a(x) a(a(x)) -> a(x) a(c(x)) -> a(x) e(d(x)) -> a(e(x)) d(c(c(x))) -> a(x) d(a(x)) -> a(x) e(c(x)) -> a(e(x)) e(a(x)) -> a(e(x)) STATISTICS: General number of iterations: 52 number of nodes: 955 number of processes: 26 time for orient: 2.36 time for rewrite: 0.18 time for deduce: 0.16 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.256997 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.03 Process Killing killed 44 exceeding best by: 71% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 308 (yes: 236, timeouts: 0) time limit for check: 2.00 termination time: 2.26 Deduction critical pair criterion: all redundant CPs in total: 344 for successful process: 0 required time: 0.01 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.01 overlaps: 0.01 maintenance: 0.00 One: 0.007927 Two: 0.000000 COMPLETE SYSTEM: c(d(x)) -> a(x) b(x) -> d(d(x)) a(d(x)) -> a(x) d(d(d(x))) -> c(c(x)) c(c(c(x))) -> a(x) c(a(x)) -> a(x) a(a(x)) -> a(x) a(c(x)) -> a(x) e(d(x)) -> a(e(x)) d(c(c(x))) -> a(x) d(a(x)) -> a(x) e(c(x)) -> a(e(x)) e(a(x)) -> a(e(x)) |
6.05 |
TPDB_thiemann27 | ∞ | ∞ | ⊥ | ∞ |
TPDB_zantema_z115 |
1.16
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 5 equalities: 111 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 1.019 time/normalization: 0.072 time/overlaps: 0.026 time/orientation constraints: 0.038 time/project: 0 time/sat: 0.017 time/update context: 0.043 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(d(x))) → c(c(c(x)))c(c(a(a(x)))) → c(c(c(x)))a(c(a(a(x)))) → c(c(c(x)))a(a(a(a(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))) |
0.28
OutputEQUATIONS:
Completion of TPDB_zantema_z115
a(a(x)) = d(c(x)) a(b(x)) = c(c(c(x))) b(b(x)) = a(c(c(x))) c(c(x)) = b(x) c(d(x)) = a(a(x)) d(d(x)) = b(a(c(x))) COMPLETE TRS: RULES: a(b(x)) -> b(b(x)) c(c(x)) -> b(x) c(d(x)) -> a(a(x)) d(d(x)) -> b(a(c(x))) d(a(a(x))) -> b(b(x)) a(c(a(a(x)))) -> b(b(x)) c(b(x)) -> b(b(x)) b(b(b(x))) -> b(b(x)) d(b(x)) -> c(a(a(x))) b(b(a(x))) -> b(b(x)) a(a(a(a(x)))) -> b(b(x)) d(c(x)) -> a(a(x)) a(a(c(x))) -> c(a(a(x))) a(a(d(x))) -> b(b(x)) b(a(a(x))) -> b(b(x)) b(c(x)) -> b(b(x)) b(d(x)) -> c(a(a(x))) SUCCESS Search time: 0.28 seconds |
12.55
OutputCOMPLETE SYSTEM: c(c(x)) -> b(x) a(a(x)) -> c(d(x)) a(b(x)) -> b(b(x)) d(c(x)) -> c(d(x)) a(c(d(x))) -> c(d(a(x))) d(b(x)) -> b(d(x)) b(c(x)) -> b(b(x)) d(d(x)) -> b(a(c(x))) c(b(x)) -> b(b(x)) b(b(b(x))) -> b(b(x)) b(b(d(x))) -> b(b(x)) b(b(a(x))) -> b(b(x)) c(d(a(c(x)))) -> b(b(x)) b(d(a(c(x)))) -> b(b(x)) c(d(a(d(x)))) -> b(b(x)) b(d(a(d(x)))) -> b(b(x)) STATISTICS: General number of iterations: 43 number of nodes: 1807 number of processes: 115 time for orient: 5.89 time for rewrite: 0.56 time for deduce: 0.56 Isomorphism Check: term permutations+ (detected automatically) time for checking: 2.783834 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.07 Process Killing killed 65 exceeding best by: 71% required time: 0.01 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 690 (yes: 551, timeouts: 0) time limit for check: 2.00 termination time: 5.58 Deduction critical pair criterion: all redundant CPs in total: 396 for successful process: 4 required time: 0.02 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.01 overlaps: 0.01 maintenance: 0.00 One: 0.039929 Two: 0.000000 COMPLETE SYSTEM: c(c(x)) -> b(x) a(a(x)) -> c(d(x)) a(b(x)) -> b(b(x)) d(c(x)) -> c(d(x)) a(c(d(x))) -> c(d(a(x))) d(b(x)) -> b(d(x)) b(c(x)) -> b(b(x)) d(d(x)) -> b(a(c(x))) c(b(x)) -> b(b(x)) b(b(b(x))) -> b(b(x)) b(b(d(x))) -> b(b(x)) b(b(a(x))) -> b(b(x)) c(d(a(c(x)))) -> b(b(x)) b(d(a(c(x)))) -> b(b(x)) c(d(a(d(x)))) -> b(b(x)) b(d(a(d(x)))) -> b(b(x)) |
7.38 |
TPTP_BOO027-1_theory |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 8 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.004 time/normalization: 0 time/overlaps: 0.003 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))) |
0.00
OutputEQUATIONS:
Completion of TPTP_BOO027-1_theory
multiply(x,add(y,z)) = add(multiply(y,x),multiply(z,x)) add(x,inverse(x)) = one() add(multiply(x,inverse(x)),add(multiply(x,y),multiply(inverse(x),y))) = y add(multiply(x,inverse(y)),add(multiply(x,y),multiply(inverse(y),y))) = x add(multiply(x,inverse(y)),add(multiply(x,x),multiply(inverse(y),x))) = x COMPLETE TRS: RULES: add(x,inverse(x)) -> one() add(multiply(x,inverse(x)),multiply(y,one())) -> y add(multiply(x,inverse(y)),multiply(y,add(x,inverse(y)))) -> x add(multiply(x,inverse(y)),multiply(x,add(x,inverse(y)))) -> x add(multiply(y,x),multiply(z,x)) -> multiply(x,add(y,z)) SUCCESS Search time: 0.00 seconds |
0.03
OutputCOMPLETE SYSTEM: add(x,inverse(x)) -> one() add(multiply(x,y),multiply(z,y)) -> multiply(y,add(x,z)) add(multiply(x,inverse(x)),multiply(y,one())) -> y add(multiply(x,inverse(y)),multiply(x,add(x,inverse(y)))) -> x add(multiply(x,inverse(x)),multiply(x,one())) -> x add(multiply(x,inverse(y)),multiply(y,add(x,inverse(y)))) -> x STATISTICS: General number of iterations: 7 number of nodes: 10 number of processes: 0 time for orient: 0.02 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 7 (yes: 6, timeouts: 0) time limit for check: 2.00 termination time: 0.02 Deduction critical pair criterion: all redundant CPs in total: 1 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000107 Two: 0.000000 COMPLETE SYSTEM: add(x,inverse(x)) -> one() add(multiply(x,y),multiply(z,y)) -> multiply(y,add(x,z)) add(multiply(x,inverse(x)),multiply(y,one())) -> y add(multiply(x,inverse(y)),multiply(x,add(x,inverse(y)))) -> x add(multiply(x,inverse(x)),multiply(x,one())) -> x add(multiply(x,inverse(y)),multiply(y,add(x,inverse(y)))) -> x |
3.39 |
TPTP_COL053-1_theory |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 1 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
OutputEQUATIONS:
Completion of TPTP_COL053-1_theory
response(compose(x,y),w) = response(x,response(y,w)) COMPLETE TRS: RULES: response(compose(x,y),w) -> response(x,response(y,w)) SUCCESS Search time: 0.00 seconds |
0.01
OutputCOMPLETE SYSTEM: response(compose(x,y),w) -> response(x,response(y,w)) STATISTICS: General number of iterations: 2 number of nodes: 4 number of processes: 1 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 2 (yes: 2, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 1 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000054 Two: 0.000000 COMPLETE SYSTEM: response(compose(x,y),w) -> response(x,response(y,w)) |
2.64 |
TPTP_COL056-1_theory |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 3 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_COL056-1_theory
(RULES response(a,c) → bresponse(a,b) → cresponse(compose(x,y),w) → response(x,response(y,w))) |
0.00
OutputEQUATIONS:
Completion of TPTP_COL056-1_theory
response(compose(x,y),w) = response(x,response(y,w)) response(a(),b()) = c() response(a(),c()) = b() COMPLETE TRS: RULES: response(compose(x,y),w) -> response(x,response(y,w)) response(a(),response(a(),c())) -> c() b() -> response(a(),c()) SUCCESS Search time: 0.00 seconds |
0.03
OutputCOMPLETE SYSTEM: response(a(),b()) -> c() response(a(),c()) -> b() response(compose(x,y),w) -> response(x,response(y,w)) STATISTICS: General number of iterations: 4 number of nodes: 12 number of processes: 5 time for orient: 0.02 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: renamings+ (detected automatically) time for checking: 0.000074 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 10 (yes: 10, timeouts: 0) time limit for check: 2.00 termination time: 0.02 Deduction critical pair criterion: all redundant CPs in total: 3 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000082 Two: 0.000000 COMPLETE SYSTEM: response(a(),b()) -> c() response(a(),c()) -> b() response(compose(x,y),w) -> response(x,response(y,w)) |
2.93 |
TPTP_COL060-1_theory |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 2 restarts: 1 time/cache: 0 time/set ops: 0 time/maxk: 0.003 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0.003 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR x y 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)) |
⊥ |
0.02
OutputCOMPLETE SYSTEM: apply(apply(t(),x),y) -> apply(y,x) apply(apply(apply(b(),x),y),z) -> apply(x,apply(y,z)) STATISTICS: General number of iterations: 3 number of nodes: 2 number of processes: 0 time for orient: 0.01 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 4 (yes: 2, timeouts: 0) time limit for check: 2.00 termination time: 0.01 Deduction critical pair criterion: all redundant CPs in total: 0 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000069 Two: 0.000000 COMPLETE SYSTEM: apply(apply(t(),x),y) -> apply(y,x) apply(apply(apply(b(),x),y),z) -> apply(x,apply(y,z)) |
⊥ |
TPTP_COL085-1_theory |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 1 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0 time/normalization: 0 time/overlaps: 0 time/orientation constraints: 0 time/project: 0 time/sat: 0 time/update context: 0 Convergent TRS(VAR )
Completion of TPTP_COL085-1_theory
(RULES response(a,class="var">,b,class="var">),class="var">, → ,class="var">,b) |
0.00
OutputEQUATIONS:
Completion of TPTP_COL085-1_theory
response(a(),b()) = b() COMPLETE TRS: RULES: response(a(),b()) -> b() SUCCESS Search time: 0.00 seconds |
0.00
OutputCOMPLETE SYSTEM: response(a(),b()) -> b() STATISTICS: General number of iterations: 2 number of nodes: 1 number of processes: 0 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 1 (yes: 1, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 0 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000051 Two: 0.000000 COMPLETE SYSTEM: response(a(),b()) -> b() |
2.21 |
TPTP_GRP010-4_theory |
0.86
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 7 equalities: 78 restarts: 0 time/cache: 0 time/set ops: 0.003 time/maxk: 0.716 time/normalization: 0.056 time/overlaps: 0.048 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.033 time/update context: 0.022 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,multiply(x,inverse(x)) → multiply(c,b)inverse(b) → cinverse(c) → binverse(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(x,multiply(inverse(x),y)) → y,multiply(b,multiply(c,x)) → x,multiply(c,multiply(b,x)) → x,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))identity → multiply(c,b)) |
0.10
OutputEQUATIONS:
Completion of TPTP_GRP010-4_theory
multiply(multiply(x,y),z) = multiply(x,multiply(y,z)) multiply(identity(),x) = x multiply(inverse(x),x) = identity() multiply(c(),b()) = identity() COMPLETE TRS: RULES: multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) multiply(inverse(x),x) -> multiply(c(),b()) multiply(x,multiply(inverse(x),y)) -> y multiply(x,multiply(c(),b())) -> x multiply(b(),multiply(c(),x)) -> x identity() -> multiply(c(),b()) multiply(c(),multiply(b(),x)) -> x multiply(inverse(y),multiply(y,x)) -> x multiply(x,inverse(x)) -> multiply(c(),b()) inverse(inverse(x)) -> x inverse(c()) -> b() multiply(b(),c()) -> multiply(c(),b()) inverse(b()) -> c() inverse(multiply(y,x)) -> multiply(inverse(x),inverse(y)) SUCCESS Search time: 0.10 seconds |
1.69
OutputCOMPLETE SYSTEM: multiply(identity(),x) -> x multiply(inverse(x),x) -> identity() multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) multiply(inverse(x),multiply(x,y)) -> y multiply(x,identity()) -> x inverse(identity()) -> identity() multiply(x,inverse(x)) -> identity() b() -> inverse(c()) multiply(x,multiply(inverse(x),y)) -> y inverse(inverse(x)) -> x inverse(multiply(x,y)) -> multiply(inverse(y),inverse(x)) STATISTICS: General number of iterations: 49 number of nodes: 609 number of processes: 27 time for orient: 1.03 time for rewrite: 0.10 time for deduce: 0.18 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.02 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 220 (yes: 193, timeouts: 0) time limit for check: 2.00 termination time: 0.99 Deduction critical pair criterion: all redundant CPs in total: 419 for successful process: 28 required time: 0.01 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.01 overlaps: 0.01 maintenance: 0.00 One: 0.006083 Two: 0.000000 COMPLETE SYSTEM: multiply(identity(),x) -> x multiply(inverse(x),x) -> identity() multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) multiply(inverse(x),multiply(x,y)) -> y multiply(x,identity()) -> x inverse(identity()) -> identity() multiply(x,inverse(x)) -> identity() b() -> inverse(c()) multiply(x,multiply(inverse(x),y)) -> y inverse(inverse(x)) -> x inverse(multiply(x,y)) -> multiply(inverse(y),inverse(x)) |
9.68 |
TPTP_GRP011-4_theory |
0.97
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 7 equalities: 70 restarts: 0 time/cache: 0 time/set ops: 0.005 time/maxk: 0.771 time/normalization: 0.075 time/overlaps: 0.057 time/orientation constraints: 0.007 time/project: 0 time/sat: 0.036 time/update context: 0.027 Convergent TRS(VAR x y z)
Completion of TPTP_GRP011-4_theory
(RULES multiply(inverse(x),x) → identitymultiply(x,inverse(x)) → identityinverse(multiply(x,y)) → multiply(inverse(y),inverse(x))b → dinverse(identity) → identityinverse(inverse(x)) → x,multiply(x,identity) → x,multiply(x,multiply(inverse(x),y)) → y,multiply(inverse(x),multiply(x,y)) → y,multiply(multiply(x,y),z) → multiply(x,multiply(y,z))multiply(identity,x) → x,) |
0.04
OutputEQUATIONS:
Completion of TPTP_GRP011-4_theory
multiply(multiply(x,y),z) = multiply(x,multiply(y,z)) multiply(identity(),x) = x multiply(inverse(x),x) = identity() multiply(b(),c()) = multiply(d(),c()) COMPLETE TRS: RULES: multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) multiply(identity(),x) -> x multiply(inverse(x),x) -> identity() multiply(x,multiply(inverse(x),y)) -> y inverse(identity()) -> identity() multiply(inverse(y),multiply(y,x)) -> x multiply(x,identity()) -> x multiply(x,inverse(x)) -> identity() d() -> b() inverse(inverse(x)) -> x inverse(multiply(y,x)) -> multiply(inverse(x),inverse(y)) SUCCESS Search time: 0.04 seconds |
0.51
OutputCOMPLETE SYSTEM: multiply(identity(),x) -> x multiply(inverse(x),x) -> identity() multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) multiply(inverse(x),multiply(x,y)) -> y multiply(x,identity()) -> x inverse(identity()) -> identity() inverse(inverse(x)) -> x multiply(x,inverse(x)) -> identity() multiply(x,multiply(inverse(x),y)) -> y b() -> d() inverse(multiply(x,y)) -> multiply(inverse(y),inverse(x)) STATISTICS: General number of iterations: 26 number of nodes: 332 number of processes: 6 time for orient: 0.36 time for rewrite: 0.03 time for deduce: 0.05 Isomorphism Check: renamings+ (detected automatically) time for checking: 0.006345 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 77 (yes: 65, timeouts: 0) time limit for check: 2.00 termination time: 0.36 Deduction critical pair criterion: all redundant CPs in total: 199 for successful process: 16 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000483 Two: 0.000000 COMPLETE SYSTEM: multiply(identity(),x) -> x multiply(inverse(x),x) -> identity() multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) multiply(inverse(x),multiply(x,y)) -> y multiply(x,identity()) -> x inverse(identity()) -> identity() inverse(inverse(x)) -> x multiply(x,inverse(x)) -> identity() multiply(x,multiply(inverse(x),y)) -> y b() -> d() inverse(multiply(x,y)) -> multiply(inverse(y),inverse(x)) |
7.34 |
TPTP_GRP012-4_theory |
0.10
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 4 equalities: 28 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.06 time/normalization: 0.011 time/overlaps: 0.015 time/orientation constraints: 0.001 time/project: 0 time/sat: 0.002 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))) |
0.01
OutputEQUATIONS:
Completion of TPTP_GRP012-4_theory
multiply(x,identity()) = x multiply(x,inverse(x)) = identity() multiply(identity(),x) = x multiply(inverse(x),x) = identity() multiply(multiply(x,y),z) = multiply(x,multiply(y,z)) COMPLETE TRS: RULES: multiply(x,identity()) -> x multiply(x,inverse(x)) -> identity() multiply(identity(),x) -> x multiply(inverse(x),x) -> identity() multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) inverse(identity()) -> identity() multiply(y,multiply(inverse(y),x)) -> x multiply(inverse(y),multiply(y,x)) -> x inverse(inverse(x)) -> x inverse(multiply(y,x)) -> multiply(inverse(x),inverse(y)) SUCCESS Search time: 0.01 seconds |
0.13
OutputCOMPLETE SYSTEM: multiply(x,identity()) -> x multiply(identity(),x) -> x multiply(x,inverse(x)) -> identity() inverse(identity()) -> identity() multiply(inverse(x),x) -> identity() multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) multiply(x,multiply(inverse(x),y)) -> y inverse(inverse(x)) -> x multiply(inverse(x),multiply(x,y)) -> y inverse(multiply(x,y)) -> multiply(inverse(y),inverse(x)) STATISTICS: General number of iterations: 17 number of nodes: 203 number of processes: 3 time for orient: 0.06 time for rewrite: 0.02 time for deduce: 0.03 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 22 (yes: 22, timeouts: 0) time limit for check: 2.00 termination time: 0.05 Deduction critical pair criterion: all redundant CPs in total: 142 for successful process: 15 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000300 Two: 0.000000 COMPLETE SYSTEM: multiply(x,identity()) -> x multiply(identity(),x) -> x multiply(x,inverse(x)) -> identity() inverse(identity()) -> identity() multiply(inverse(x),x) -> identity() multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) multiply(x,multiply(inverse(x),y)) -> y inverse(inverse(x)) -> x multiply(inverse(x),multiply(x,y)) -> y inverse(multiply(x,y)) -> multiply(inverse(y),inverse(x)) |
5.31 |
TPTP_GRP393-2_theory |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 1 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
OutputEQUATIONS:
Completion of TPTP_GRP393-2_theory
multiply(multiply(x,y),z) = multiply(x,multiply(y,z)) COMPLETE TRS: RULES: multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) SUCCESS Search time: 0.00 seconds |
0.01
OutputCOMPLETE SYSTEM: multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) STATISTICS: General number of iterations: 2 number of nodes: 6 number of processes: 1 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 2 (yes: 2, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 2 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000053 Two: 0.000000 COMPLETE SYSTEM: multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) |
2.17 |
TPTP_GRP394-3_theory |
0.27
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 6 equalities: 44 restarts: 0 time/cache: 0 time/set ops: 0.001 time/maxk: 0.202 time/normalization: 0.023 time/overlaps: 0.025 time/orientation constraints: 0.002 time/project: 0 time/sat: 0.007 time/update context: 0.007 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))) |
0.02
OutputEQUATIONS:
Completion of TPTP_GRP394-3_theory
multiply(identity(),x) = x multiply(inverse(x),x) = identity() multiply(multiply(x,y),z) = multiply(x,multiply(y,z)) COMPLETE TRS: RULES: multiply(identity(),x) -> x multiply(inverse(x),x) -> identity() multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) multiply(x,multiply(inverse(x),y)) -> y inverse(identity()) -> identity() multiply(inverse(y),multiply(y,x)) -> x multiply(x,identity()) -> x multiply(x,inverse(x)) -> identity() inverse(inverse(x)) -> x inverse(multiply(y,x)) -> multiply(inverse(x),inverse(y)) SUCCESS Search time: 0.02 seconds |
0.27
OutputCOMPLETE SYSTEM: multiply(identity(),x) -> x multiply(inverse(x),x) -> identity() multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) multiply(inverse(x),multiply(x,y)) -> y multiply(x,identity()) -> x inverse(identity()) -> identity() inverse(inverse(x)) -> x multiply(x,inverse(x)) -> identity() multiply(x,multiply(inverse(x),y)) -> y inverse(multiply(x,y)) -> multiply(inverse(y),inverse(x)) STATISTICS: General number of iterations: 21 number of nodes: 222 number of processes: 3 time for orient: 0.16 time for rewrite: 0.02 time for deduce: 0.05 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 35 (yes: 32, timeouts: 0) time limit for check: 2.00 termination time: 0.16 Deduction critical pair criterion: all redundant CPs in total: 153 for successful process: 13 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000528 Two: 0.000000 COMPLETE SYSTEM: multiply(identity(),x) -> x multiply(inverse(x),x) -> identity() multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) multiply(inverse(x),multiply(x,y)) -> y multiply(x,identity()) -> x inverse(identity()) -> identity() inverse(inverse(x)) -> x multiply(x,inverse(x)) -> identity() multiply(x,multiply(inverse(x),y)) -> y inverse(multiply(x,y)) -> multiply(inverse(y),inverse(x)) |
5.63 |
TPTP_GRP454-1_theory |
26.16
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 15 equalities: 191 restarts: 1 time/cache: 0 time/set ops: 0.021 time/maxk: 24.778 time/normalization: 0.553 time/overlaps: 0.409 time/orientation constraints: 1.334 time/project: 0 time/sat: 9.319 time/update context: 0.349 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,) |
1.03
OutputEQUATIONS:
Completion of TPTP_GRP454-1_theory
divide(divide(identity(),divide(a,divide(b,divide(divide(divide(a,a),a),c)))),c) = b multiply(a,b) = divide(a,divide(identity(),b)) inverse(a) = divide(identity(),a) identity() = divide(a,a) COMPLETE TRS: RULES: multiply(inverse(x),x) -> identity() multiply(x,inverse(x)) -> identity() multiply(inverse(x),multiply(x,y)) -> y multiply(x,multiply(inverse(x),y)) -> y divide(x,y) -> multiply(x,inverse(y)) multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) inverse(identity()) -> identity() multiply(identity(),x) -> x inverse(inverse(x)) -> x multiply(x,identity()) -> x inverse(multiply(y,x)) -> multiply(inverse(x),inverse(y)) SUCCESS Search time: 1.03 seconds |
1.26
OutputCOMPLETE SYSTEM: divide(identity(),a) -> inverse(a) divide(a,a) -> identity() inverse(identity()) -> identity() multiply(a,b) -> divide(a,inverse(b)) divide(a,identity()) -> a inverse(inverse(a)) -> a divide(b,divide(a,inverse(b))) -> inverse(a) inverse(divide(a,b)) -> divide(b,a) divide(inverse(b),divide(a,b)) -> inverse(a) divide(divide(a,b),c) -> divide(a,divide(c,inverse(b))) divide(c,divide(b,divide(inverse(c),a))) -> divide(inverse(a),b) divide(inverse(a),divide(b,divide(a,c))) -> divide(inverse(c),b) STATISTICS: General number of iterations: 41 number of nodes: 496 number of processes: 12 time for orient: 0.70 time for rewrite: 0.09 time for deduce: 0.10 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.01 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 123 (yes: 100, timeouts: 0) time limit for check: 2.00 termination time: 0.67 Deduction critical pair criterion: all redundant CPs in total: 327 for successful process: 34 required time: 0.01 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.01 maintenance: 0.00 One: 0.004743 Two: 0.000000 COMPLETE SYSTEM: divide(identity(),a) -> inverse(a) divide(a,a) -> identity() inverse(identity()) -> identity() multiply(a,b) -> divide(a,inverse(b)) divide(a,identity()) -> a inverse(inverse(a)) -> a divide(b,divide(a,inverse(b))) -> inverse(a) inverse(divide(a,b)) -> divide(b,a) divide(inverse(b),divide(a,b)) -> inverse(a) divide(divide(a,b),c) -> divide(a,divide(c,inverse(b))) divide(c,divide(b,divide(inverse(c),a))) -> divide(inverse(a),b) divide(inverse(a),divide(b,divide(a,c))) -> divide(inverse(c),b) |
11.43 |
TPTP_GRP457-1_theory |
46.58
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 18 equalities: 243 restarts: 1 time/cache: 0 time/set ops: 0.037 time/maxk: 45.343 time/normalization: 0.535 time/overlaps: 0.445 time/orientation constraints: 1.376 time/project: 0 time/sat: 15.542 time/update context: 0.746 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,inverse(b)) → identitymultiply(b,multiply(inverse(b),a)) → a,multiply(b,identity) → b,multiply(identity,b) → b,inverse(identity) → identitymultiply(inverse(b),b) → identityinverse(inverse(b)) → b,) |
1.12
OutputEQUATIONS:
Completion of TPTP_GRP457-1_theory
divide(divide(divide(a,a),divide(a,divide(b,divide(divide(identity(),a),c)))),c) = b multiply(a,b) = divide(a,divide(identity(),b)) inverse(a) = divide(identity(),a) identity() = divide(a,a) COMPLETE TRS: RULES: multiply(inverse(x),x) -> identity() multiply(x,inverse(x)) -> identity() multiply(inverse(x),multiply(x,y)) -> y multiply(x,multiply(inverse(x),y)) -> y divide(x,y) -> multiply(x,inverse(y)) multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) inverse(identity()) -> identity() inverse(inverse(x)) -> x multiply(identity(),x) -> x multiply(x,identity()) -> x inverse(multiply(y,x)) -> multiply(inverse(x),inverse(y)) SUCCESS Search time: 1.12 seconds |
1.34
OutputCOMPLETE SYSTEM: divide(identity(),a) -> inverse(a) divide(a,a) -> identity() inverse(identity()) -> identity() multiply(a,b) -> divide(a,inverse(b)) divide(a,identity()) -> a inverse(inverse(a)) -> a divide(b,divide(a,inverse(b))) -> inverse(a) inverse(divide(a,b)) -> divide(b,a) divide(inverse(b),divide(a,b)) -> inverse(a) divide(divide(a,b),c) -> divide(a,divide(c,inverse(b))) divide(c,divide(b,divide(inverse(c),a))) -> divide(inverse(a),b) divide(inverse(a),divide(b,divide(a,c))) -> divide(inverse(c),b) STATISTICS: General number of iterations: 41 number of nodes: 496 number of processes: 12 time for orient: 0.71 time for rewrite: 0.10 time for deduce: 0.12 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.02 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 123 (yes: 100, timeouts: 0) time limit for check: 2.00 termination time: 0.68 Deduction critical pair criterion: all redundant CPs in total: 327 for successful process: 34 required time: 0.01 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.01 overlaps: 0.01 maintenance: 0.00 One: 0.004218 Two: 0.000000 COMPLETE SYSTEM: divide(identity(),a) -> inverse(a) divide(a,a) -> identity() inverse(identity()) -> identity() multiply(a,b) -> divide(a,inverse(b)) divide(a,identity()) -> a inverse(inverse(a)) -> a divide(b,divide(a,inverse(b))) -> inverse(a) inverse(divide(a,b)) -> divide(b,a) divide(inverse(b),divide(a,b)) -> inverse(a) divide(divide(a,b),c) -> divide(a,divide(c,inverse(b))) divide(c,divide(b,divide(inverse(c),a))) -> divide(inverse(a),b) divide(inverse(a),divide(b,divide(a,c))) -> divide(inverse(c),b) |
10.08 |
TPTP_GRP460-1_theory |
164.08
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 34 equalities: 175 restarts: 2 time/cache: 0 time/set ops: 0.127 time/maxk: 149.447 time/normalization: 8.961 time/overlaps: 1.716 time/orientation constraints: 3.004 time/project: 0 time/sat: 48.54 time/update context: 2.253 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)) → identityinverse(inverse(b)) → b,multiply(b,identity) → b,multiply(b,multiply(inverse(b),a)) → a,inverse(identity) → identitymultiply(inverse(b),b) → identity) |
0.20
OutputEQUATIONS:
Completion of TPTP_GRP460-1_theory
divide(a,divide(divide(divide(identity(),b),c),divide(divide(divide(a,a),a),c))) = b multiply(a,b) = divide(a,divide(identity(),b)) inverse(a) = divide(identity(),a) identity() = divide(a,a) COMPLETE TRS: RULES: multiply(identity(),x) -> x multiply(inverse(x),x) -> identity() multiply(x,inverse(x)) -> identity() divide(x,y) -> multiply(x,inverse(y)) multiply(inverse(x),multiply(x,y)) -> y inverse(identity()) -> identity() inverse(inverse(x)) -> x multiply(x,identity()) -> x multiply(y,multiply(inverse(y),x)) -> x inverse(multiply(y,x)) -> multiply(inverse(x),inverse(y)) multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) SUCCESS Search time: 0.20 seconds |
⊥ | 10.44 |
TPTP_GRP463-1_theory |
40.06
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 18 equalities: 205 restarts: 1 time/cache: 0 time/set ops: 0.031 time/maxk: 38.813 time/normalization: 0.467 time/overlaps: 0.399 time/orientation constraints: 0.94 time/project: 0 time/sat: 18.047 time/update context: 0.586 Convergent TRS(VAR b a c)
Completion of TPTP_GRP463-1_theory
(RULES multiply(identity,b) → b,divide(b,a) → multiply(b,inverse(a))inverse(inverse(b)) → b,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,identity) → b,multiply(b,multiply(inverse(b),a)) → a,inverse(identity) → identitymultiply(inverse(b),b) → identity) |
0.55
OutputEQUATIONS:
Completion of TPTP_GRP463-1_theory
divide(a,divide(divide(divide(divide(a,a),b),c),divide(divide(identity(),a),c))) = b multiply(a,b) = divide(a,divide(identity(),b)) inverse(a) = divide(identity(),a) identity() = divide(a,a) COMPLETE TRS: RULES: multiply(inverse(x),x) -> identity() multiply(x,inverse(x)) -> identity() multiply(inverse(x),multiply(x,y)) -> y multiply(x,multiply(inverse(x),y)) -> y divide(x,y) -> multiply(x,inverse(y)) inverse(identity()) -> identity() inverse(inverse(x)) -> x multiply(x,identity()) -> x multiply(identity(),x) -> x inverse(multiply(y,x)) -> multiply(inverse(x),inverse(y)) multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) SUCCESS Search time: 0.55 seconds |
⊥ | 8.81 |
TPTP_GRP481-1_theory |
28.59
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 13 equalities: 212 restarts: 0 time/cache: 0 time/set ops: 0.05 time/maxk: 27.212 time/normalization: 0.755 time/overlaps: 0.301 time/orientation constraints: 0.052 time/project: 0 time/sat: 0.767 time/update context: 0.862 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),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,inverse(identity) → identitymultiply(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(c,lass="var">c,identity) → c,multiply(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,) |
0.60
OutputEQUATIONS:
Completion of TPTP_GRP481-1_theory
double_divide(double_divide(double_divide(a,double_divide(b,identity())),double_divide(double_divide(c,double_divide(d,double_divide(d,identity()))),double_divide(a,identity()))),b) = c multiply(a,b) = double_divide(double_divide(b,a),identity()) inverse(a) = double_divide(a,identity()) identity() = double_divide(a,inverse(a)) COMPLETE TRS: RULES: multiply(x,inverse(x)) -> identity() inverse(inverse(x)) -> x multiply(inverse(x),x) -> identity() multiply(inverse(x),multiply(x,y)) -> y multiply(x,multiply(inverse(x),y)) -> y multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) inverse(identity()) -> identity() multiply(x,identity()) -> x multiply(identity(),x) -> x double_divide(y,x) -> multiply(inverse(y),inverse(x)) inverse(multiply(y,x)) -> multiply(inverse(x),inverse(y)) SUCCESS Search time: 0.60 seconds |
11.72
OutputCOMPLETE SYSTEM: double_divide(a,identity()) -> inverse(a) double_divide(a,inverse(a)) -> identity() inverse(identity()) -> identity() double_divide(inverse(a),a) -> identity() inverse(inverse(a)) -> a double_divide(identity(),a) -> inverse(a) double_divide(a,double_divide(b,a)) -> b inverse(double_divide(a,b)) -> double_divide(inverse(b),inverse(a)) double_divide(inverse(a),double_divide(b,double_divide(a,c))) -> double_divide(c,inverse(b)) multiply(a,b) -> double_divide(inverse(a),inverse(b)) double_divide(double_divide(c,a),b) -> double_divide(inverse(a),double_divide(inverse(b),c)) double_divide(c,double_divide(b,double_divide(inverse(c),a))) -> double_divide(a,inverse(b)) STATISTICS: General number of iterations: 142 number of nodes: 4092 number of processes: 16 time for orient: 2.71 time for rewrite: 1.11 time for deduce: 0.90 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.15 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 302 (yes: 228, timeouts: 0) time limit for check: 2.00 termination time: 2.44 Deduction critical pair criterion: all redundant CPs in total: 2448 for successful process: 53 required time: 0.14 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.02 encompassments: 0.05 overlaps: 0.06 maintenance: 0.00 One: 0.034547 Two: 0.000000 COMPLETE SYSTEM: double_divide(a,identity()) -> inverse(a) double_divide(a,inverse(a)) -> identity() inverse(identity()) -> identity() double_divide(inverse(a),a) -> identity() inverse(inverse(a)) -> a double_divide(identity(),a) -> inverse(a) double_divide(a,double_divide(b,a)) -> b inverse(double_divide(a,b)) -> double_divide(inverse(b),inverse(a)) double_divide(inverse(a),double_divide(b,double_divide(a,c))) -> double_divide(c,inverse(b)) multiply(a,b) -> double_divide(inverse(a),inverse(b)) double_divide(double_divide(c,a),b) -> double_divide(inverse(a),double_divide(inverse(b),c)) double_divide(c,double_divide(b,double_divide(inverse(c),a))) -> double_divide(a,inverse(b)) |
9.14 |
TPTP_GRP484-1_theory |
28.47
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 14 equalities: 210 restarts: 0 time/cache: 0 time/set ops: 0.049 time/maxk: 27.083 time/normalization: 0.673 time/overlaps: 0.373 time/orientation constraints: 0.05 time/project: 0 time/sat: 0.626 time/update context: 0.69 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,) |
0.29
OutputEQUATIONS:
Completion of TPTP_GRP484-1_theory
double_divide(double_divide(a,double_divide(double_divide(double_divide(a,b),c),double_divide(b,identity()))),double_divide(identity(),identity())) = c multiply(a,b) = double_divide(double_divide(b,a),identity()) inverse(a) = double_divide(a,identity()) identity() = double_divide(a,inverse(a)) COMPLETE TRS: RULES: inverse(inverse(x)) -> x multiply(x,identity()) -> x multiply(x,inverse(x)) -> identity() multiply(x,multiply(inverse(x),y)) -> y multiply(inverse(x),x) -> identity() multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) inverse(identity()) -> identity() multiply(inverse(y),multiply(y,x)) -> x double_divide(y,x) -> multiply(inverse(y),inverse(x)) inverse(multiply(y,x)) -> multiply(inverse(x),inverse(y)) multiply(identity(),x) -> x SUCCESS Search time: 0.29 seconds |
42.12
OutputCOMPLETE SYSTEM: multiply(a,inverse(a)) -> identity() inverse(multiply(a,b)) -> multiply(inverse(b),inverse(a)) multiply(inverse(a),multiply(a,b)) -> b multiply(multiply(a,b),c) -> multiply(a,multiply(b,c)) multiply(a,multiply(inverse(a),b)) -> b double_divide(a,b) -> multiply(inverse(a),inverse(b)) multiply(a,identity()) -> a multiply(identity(),a) -> a inverse(identity()) -> identity() inverse(inverse(a)) -> a multiply(inverse(a),a) -> identity() STATISTICS: General number of iterations: 248 number of nodes: 5948 number of processes: 3 time for orient: 14.17 time for rewrite: 2.49 time for deduce: 3.19 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.36 Process Killing killed 36 exceeding best by: 71% required time: 0.01 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 1035 (yes: 775, timeouts: 0) time limit for check: 2.00 termination time: 13.07 Deduction critical pair criterion: all redundant CPs in total: 4839 for successful process: 157 required time: 0.39 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.05 encompassments: 0.10 overlaps: 0.13 maintenance: 0.01 One: 0.116956 Two: 0.000000 COMPLETE SYSTEM: multiply(a,inverse(a)) -> identity() inverse(multiply(a,b)) -> multiply(inverse(b),inverse(a)) multiply(inverse(a),multiply(a,b)) -> b multiply(multiply(a,b),c) -> multiply(a,multiply(b,c)) multiply(a,multiply(inverse(a),b)) -> b double_divide(a,b) -> multiply(inverse(a),inverse(b)) multiply(a,identity()) -> a multiply(identity(),a) -> a inverse(identity()) -> identity() inverse(inverse(a)) -> a multiply(inverse(a),a) -> identity() |
10.97 |
TPTP_GRP487-1_theory |
46.40
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 18 equalities: 225 restarts: 0 time/cache: 0 time/set ops: 0.07 time/maxk: 44.521 time/normalization: 0.961 time/overlaps: 0.409 time/orientation constraints: 0.058 time/project: 0 time/sat: 0.961 time/update context: 1.039 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) |
0.51
OutputEQUATIONS:
Completion of TPTP_GRP487-1_theory
double_divide(a,double_divide(double_divide(double_divide(identity(),double_divide(double_divide(a,identity()),double_divide(b,c))),b),identity())) = c multiply(a,b) = double_divide(double_divide(b,a),identity()) inverse(a) = double_divide(a,identity()) identity() = double_divide(a,inverse(a)) COMPLETE TRS: RULES: inverse(identity()) -> identity() inverse(inverse(x)) -> x multiply(x,identity()) -> x multiply(identity(),x) -> x multiply(x,inverse(x)) -> identity() multiply(inverse(x),multiply(x,y)) -> y inverse(multiply(x,y)) -> multiply(inverse(y),inverse(x)) multiply(inverse(x),x) -> identity() double_divide(y,x) -> multiply(inverse(y),inverse(x)) multiply(y,multiply(inverse(y),x)) -> x multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) SUCCESS Search time: 0.51 seconds |
26.74
OutputCOMPLETE SYSTEM: double_divide(a,identity()) -> inverse(a) double_divide(a,inverse(a)) -> identity() inverse(identity()) -> identity() double_divide(inverse(a),a) -> identity() inverse(double_divide(a,b)) -> double_divide(inverse(b),inverse(a)) inverse(inverse(a)) -> a double_divide(identity(),a) -> inverse(a) multiply(a,b) -> double_divide(inverse(a),inverse(b)) double_divide(a,double_divide(b,a)) -> b double_divide(double_divide(c,a),b) -> double_divide(inverse(a),double_divide(inverse(b),c)) double_divide(inverse(a),double_divide(b,double_divide(a,c))) -> double_divide(c,inverse(b)) double_divide(c,double_divide(b,double_divide(inverse(c),a))) -> double_divide(a,inverse(b)) STATISTICS: General number of iterations: 197 number of nodes: 3777 number of processes: 3 time for orient: 8.47 time for rewrite: 1.49 time for deduce: 1.99 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.26 Process Killing killed 35 exceeding best by: 71% required time: 0.01 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 795 (yes: 617, timeouts: 0) time limit for check: 2.00 termination time: 7.78 Deduction critical pair criterion: all redundant CPs in total: 2832 for successful process: 154 required time: 0.20 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.03 encompassments: 0.06 overlaps: 0.09 maintenance: 0.01 One: 0.090436 Two: 0.000000 COMPLETE SYSTEM: double_divide(a,identity()) -> inverse(a) double_divide(a,inverse(a)) -> identity() inverse(identity()) -> identity() double_divide(inverse(a),a) -> identity() inverse(double_divide(a,b)) -> double_divide(inverse(b),inverse(a)) inverse(inverse(a)) -> a double_divide(identity(),a) -> inverse(a) multiply(a,b) -> double_divide(inverse(a),inverse(b)) double_divide(a,double_divide(b,a)) -> b double_divide(double_divide(c,a),b) -> double_divide(inverse(a),double_divide(inverse(b),c)) double_divide(inverse(a),double_divide(b,double_divide(a,c))) -> double_divide(c,inverse(b)) double_divide(c,double_divide(b,double_divide(inverse(c),a))) -> double_divide(a,inverse(b)) |
13.59 |
TPTP_GRP490-1_theory |
19.88
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 13 equalities: 182 restarts: 0 time/cache: 0 time/set ops: 0.049 time/maxk: 18.868 time/normalization: 0.523 time/overlaps: 0.226 time/orientation constraints: 0.035 time/project: 0 time/sat: 0.364 time/update context: 0.495 Convergent TRS(VAR c a b)
Completion of TPTP_GRP490-1_theory
(RULES double_divide(c,lass="var">c,c,lass="var">a) → multiply(inverse(c,lass="var">c),inverse(c,lass="var">a))multiply(multiply(c,lass="var">c,c,lass="var">a),c,lass="var">b) → multiply(c,lass="var">c,multiply(c,lass="var">a,c,lass="var">b))multiply(c,lass="var">c,multiply(inverse(c,lass="var">c),c,lass="var">a)) → c,lass="var">a,multiply(inverse(c,lass="var">c),multiply(c,lass="var">c,c,lass="var">a)) → c,lass="var">a,inverse(multiply(c,lass="var">c,c,lass="var">a)) → multiply(inverse(c,lass="var">a),inverse(c,lass="var">c))multiply(identity,c,lass="var">c) → c,multiply(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(inverse(c,lass="var">c),c,lass="var">c) → identityinverse(identity) → identitymultiply(c,lass="var">c,identity) → c,inverse(inverse(c,lass="var">c)) → c,) |
2.46
OutputEQUATIONS:
Completion of TPTP_GRP490-1_theory
double_divide(double_divide(identity(),a),double_divide(identity(),double_divide(double_divide(double_divide(a,b),identity()),double_divide(c,b)))) = c multiply(a,b) = double_divide(double_divide(b,a),identity()) inverse(a) = double_divide(a,identity()) identity() = double_divide(a,inverse(a)) COMPLETE TRS: RULES: inverse(inverse(x)) -> x inverse(identity()) -> identity() multiply(x,identity()) -> x multiply(x,inverse(x)) -> identity() multiply(x,multiply(inverse(x),y)) -> y multiply(inverse(x),multiply(x,y)) -> y multiply(inverse(x),x) -> identity() double_divide(y,x) -> multiply(inverse(y),inverse(x)) multiply(identity(),x) -> x inverse(multiply(y,x)) -> multiply(inverse(x),inverse(y)) multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) SUCCESS Search time: 2.46 seconds |
29.91
OutputCOMPLETE SYSTEM: double_divide(a,identity()) -> inverse(a) double_divide(a,inverse(a)) -> identity() inverse(identity()) -> identity() inverse(inverse(a)) -> a double_divide(inverse(a),a) -> identity() double_divide(identity(),a) -> inverse(a) double_divide(a,double_divide(b,a)) -> b multiply(a,b) -> double_divide(inverse(a),inverse(b)) inverse(double_divide(a,b)) -> double_divide(inverse(b),inverse(a)) double_divide(double_divide(c,a),b) -> double_divide(inverse(a),double_divide(inverse(b),c)) double_divide(c,double_divide(b,double_divide(inverse(c),a))) -> double_divide(a,inverse(b)) double_divide(inverse(a),double_divide(b,double_divide(a,c))) -> double_divide(c,inverse(b)) STATISTICS: General number of iterations: 218 number of nodes: 3517 number of processes: 30 time for orient: 6.06 time for rewrite: 1.72 time for deduce: 1.70 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.29 Process Killing killed 0 exceeding best by: 401% required time: 0.01 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 625 (yes: 469, timeouts: 0) time limit for check: 2.00 termination time: 5.37 Deduction critical pair criterion: all redundant CPs in total: 3057 for successful process: 198 required time: 0.20 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.04 encompassments: 0.07 overlaps: 0.10 maintenance: 0.01 One: 0.086518 Two: 0.000000 COMPLETE SYSTEM: double_divide(a,identity()) -> inverse(a) double_divide(a,inverse(a)) -> identity() inverse(identity()) -> identity() inverse(inverse(a)) -> a double_divide(inverse(a),a) -> identity() double_divide(identity(),a) -> inverse(a) double_divide(a,double_divide(b,a)) -> b multiply(a,b) -> double_divide(inverse(a),inverse(b)) inverse(double_divide(a,b)) -> double_divide(inverse(b),inverse(a)) double_divide(double_divide(c,a),b) -> double_divide(inverse(a),double_divide(inverse(b),c)) double_divide(c,double_divide(b,double_divide(inverse(c),a))) -> double_divide(a,inverse(b)) double_divide(inverse(a),double_divide(b,double_divide(a,c))) -> double_divide(c,inverse(b)) |
10.18 |
TPTP_GRP493-1_theory |
167.07
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 25 equalities: 264 restarts: 1 time/cache: 0 time/set ops: 0.103 time/maxk: 164.129 time/normalization: 1.186 time/overlaps: 0.576 time/orientation constraints: 2.263 time/project: 0 time/sat: 95.787 time/update context: 1.338 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(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,) |
2.06
OutputEQUATIONS:
Completion of TPTP_GRP493-1_theory
double_divide(double_divide(identity(),a),double_divide(double_divide(double_divide(b,c),double_divide(identity(),identity())),double_divide(a,c))) = b multiply(a,b) = double_divide(double_divide(b,a),identity()) inverse(a) = double_divide(a,identity()) identity() = double_divide(a,inverse(a)) COMPLETE TRS: RULES: inverse(identity()) -> identity() multiply(x,identity()) -> x multiply(identity(),x) -> x multiply(x,multiply(inverse(x),y)) -> y multiply(inverse(x),x) -> identity() inverse(inverse(x)) -> x multiply(x,inverse(x)) -> identity() double_divide(y,x) -> multiply(inverse(y),inverse(x)) multiply(inverse(y),multiply(y,x)) -> x inverse(multiply(y,x)) -> multiply(inverse(x),inverse(y)) multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) SUCCESS Search time: 2.06 seconds |
23.23
OutputCOMPLETE SYSTEM: double_divide(a,identity()) -> inverse(a) double_divide(a,inverse(a)) -> identity() inverse(identity()) -> identity() double_divide(identity(),a) -> inverse(a) inverse(inverse(a)) -> a double_divide(inverse(a),a) -> identity() inverse(double_divide(a,b)) -> double_divide(inverse(b),inverse(a)) double_divide(a,double_divide(b,a)) -> b double_divide(double_divide(c,a),b) -> double_divide(inverse(a),double_divide(inverse(b),c)) double_divide(c,double_divide(b,double_divide(inverse(c),a))) -> double_divide(a,inverse(b)) double_divide(inverse(a),double_divide(b,double_divide(a,c))) -> double_divide(c,inverse(b)) multiply(a,b) -> double_divide(inverse(a),inverse(b)) STATISTICS: General number of iterations: 241 number of nodes: 8700 number of processes: 0 time for orient: 7.72 time for rewrite: 2.50 time for deduce: 2.17 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.20 Process Killing killed 13 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 483 (yes: 254, timeouts: 0) time limit for check: 2.00 termination time: 7.05 Deduction critical pair criterion: all redundant CPs in total: 5644 for successful process: 107 required time: 0.41 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.03 encompassments: 0.10 overlaps: 0.17 maintenance: 0.00 One: 0.035643 Two: 0.000000 COMPLETE SYSTEM: double_divide(a,identity()) -> inverse(a) double_divide(a,inverse(a)) -> identity() inverse(identity()) -> identity() double_divide(identity(),a) -> inverse(a) inverse(inverse(a)) -> a double_divide(inverse(a),a) -> identity() inverse(double_divide(a,b)) -> double_divide(inverse(b),inverse(a)) double_divide(a,double_divide(b,a)) -> b double_divide(double_divide(c,a),b) -> double_divide(inverse(a),double_divide(inverse(b),c)) double_divide(c,double_divide(b,double_divide(inverse(c),a))) -> double_divide(a,inverse(b)) double_divide(inverse(a),double_divide(b,double_divide(a,c))) -> double_divide(c,inverse(b)) multiply(a,b) -> double_divide(inverse(a),inverse(b)) |
9.51 |
TPTP_GRP496-1_theory |
195.97
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 22 equalities: 238 restarts: 1 time/cache: 0 time/set ops: 0.038 time/maxk: 191.923 time/normalization: 2.133 time/overlaps: 0.715 time/orientation constraints: 3.694 time/project: 0 time/sat: 141.459 time/update context: 0.837 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,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(c,lass="var">c,inverse(c,lass="var">c)) → identitymultiply(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,) |
0.33
OutputEQUATIONS:
Completion of TPTP_GRP496-1_theory
double_divide(double_divide(identity(),double_divide(a,double_divide(b,identity()))),double_divide(double_divide(b,double_divide(c,a)),identity())) = c multiply(a,b) = double_divide(double_divide(b,a),identity()) inverse(a) = double_divide(a,identity()) identity() = double_divide(a,inverse(a)) COMPLETE TRS: RULES: inverse(inverse(x)) -> x multiply(identity(),x) -> x multiply(x,multiply(inverse(x),y)) -> y multiply(inverse(x),multiply(x,y)) -> y inverse(multiply(x,y)) -> multiply(inverse(y),inverse(x)) multiply(multiply(x,y),z) -> multiply(x,multiply(y,z)) inverse(identity()) -> identity() multiply(inverse(x),x) -> identity() multiply(x,inverse(x)) -> identity() double_divide(y,x) -> multiply(inverse(y),inverse(x)) multiply(x,identity()) -> x SUCCESS Search time: 0.33 seconds |
29.50
OutputCOMPLETE SYSTEM: double_divide(a,identity()) -> inverse(a) double_divide(a,inverse(a)) -> identity() inverse(identity()) -> identity() inverse(inverse(a)) -> a double_divide(identity(),a) -> inverse(a) double_divide(inverse(a),a) -> identity() multiply(a,b) -> double_divide(inverse(a),inverse(b)) double_divide(inverse(a),double_divide(b,double_divide(a,c))) -> double_divide(c,inverse(b)) inverse(double_divide(a,b)) -> double_divide(inverse(b),inverse(a)) double_divide(a,double_divide(b,a)) -> b double_divide(double_divide(c,a),b) -> double_divide(inverse(a),double_divide(inverse(b),c)) double_divide(c,double_divide(b,double_divide(inverse(c),a))) -> double_divide(a,inverse(b)) STATISTICS: General number of iterations: 227 number of nodes: 4870 number of processes: 21 time for orient: 8.33 time for rewrite: 2.17 time for deduce: 1.98 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.31 Process Killing killed 0 exceeding best by: 401% required time: 0.01 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 651 (yes: 491, timeouts: 0) time limit for check: 2.00 termination time: 7.58 Deduction critical pair criterion: all redundant CPs in total: 4401 for successful process: 370 required time: 0.27 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.05 encompassments: 0.09 overlaps: 0.11 maintenance: 0.01 One: 0.082175 Two: 0.000000 COMPLETE SYSTEM: double_divide(a,identity()) -> inverse(a) double_divide(a,inverse(a)) -> identity() inverse(identity()) -> identity() inverse(inverse(a)) -> a double_divide(identity(),a) -> inverse(a) double_divide(inverse(a),a) -> identity() multiply(a,b) -> double_divide(inverse(a),inverse(b)) double_divide(inverse(a),double_divide(b,double_divide(a,c))) -> double_divide(c,inverse(b)) inverse(double_divide(a,b)) -> double_divide(inverse(b),inverse(a)) double_divide(a,double_divide(b,a)) -> b double_divide(double_divide(c,a),b) -> double_divide(inverse(a),double_divide(inverse(b),c)) double_divide(c,double_divide(b,double_divide(inverse(c),a))) -> double_divide(a,inverse(b)) |
11.09 |
TPTP_HWC004-1_theory |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 10 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 )
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
OutputEQUATIONS:
Completion of TPTP_HWC004-1_theory
and_(n0(),n0()) = n0() and_(n0(),n1()) = n0() and_(n1(),n0()) = n0() and_(n1(),n1()) = n1() or_(n0(),n0()) = n0() or_(n0(),n1()) = n1() or_(n1(),n0()) = n1() or_(n1(),n1()) = n1() not_(n0()) = n1() not_(n1()) = n0() COMPLETE TRS: RULES: and_(n1(),n1()) -> n1() or_(n1(),n1()) -> n1() not_(not_(n1())) -> n1() or_(not_(n1()),n1()) -> n1() or_(n1(),not_(n1())) -> n1() and_(not_(n1()),n1()) -> not_(n1()) and_(n1(),not_(n1())) -> not_(n1()) and_(not_(n1()),not_(n1())) -> not_(n1()) or_(not_(n1()),not_(n1())) -> not_(n1()) n0() -> not_(n1()) SUCCESS Search time: 0.00 seconds |
0.06
OutputCOMPLETE SYSTEM: not(n0()) -> n1() not(n1()) -> n0() and(n0(),n0()) -> n0() and(n1(),n1()) -> n1() or(n0(),n0()) -> n0() or(n1(),n1()) -> n1() and(n0(),n1()) -> n0() and(n1(),n0()) -> n0() or(n0(),n1()) -> n1() or(n1(),n0()) -> n1() STATISTICS: General number of iterations: 11 number of nodes: 36 number of processes: 2 time for orient: 0.02 time for rewrite: 0.01 time for deduce: 0.00 Isomorphism Check: renamings+ (detected automatically) time for checking: 0.001083 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 16 (yes: 16, timeouts: 0) time limit for check: 2.00 termination time: 0.02 Deduction critical pair criterion: all redundant CPs in total: 0 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000457 Two: 0.000000 COMPLETE SYSTEM: not(n0()) -> n1() not(n1()) -> n0() and(n0(),n0()) -> n0() and(n1(),n1()) -> n1() or(n0(),n0()) -> n0() or(n1(),n1()) -> n1() and(n0(),n1()) -> n0() and(n1(),n0()) -> n0() or(n0(),n1()) -> n1() or(n1(),n0()) -> n1() |
2.52 |
TPTP_HWC004-2_theory |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 6 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) |
0.00
OutputEQUATIONS:
Completion of TPTP_HWC004-2_theory
and_(x,n0()) = n0() and_(x,n1()) = x or_(x,n0()) = x or_(x,n1()) = n1() not_(n0()) = n1() not_(n1()) = n0() COMPLETE TRS: RULES: and_(x,n1()) -> x or_(x,n1()) -> n1() not_(not_(n1())) -> n1() or_(x,not_(n1())) -> x and_(x,not_(n1())) -> not_(n1()) n0() -> not_(n1()) SUCCESS Search time: 0.00 seconds |
0.02
OutputCOMPLETE SYSTEM: not(n0()) -> n1() not(n1()) -> n0() and(x,n0()) -> n0() and(x,n1()) -> x or(x,n0()) -> x or(x,n1()) -> n1() STATISTICS: General number of iterations: 7 number of nodes: 14 number of processes: 2 time for orient: 0.01 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: renamings+ (detected automatically) time for checking: 0.000158 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 12 (yes: 12, timeouts: 0) time limit for check: 2.00 termination time: 0.01 Deduction critical pair criterion: all redundant CPs in total: 0 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000183 Two: 0.000000 COMPLETE SYSTEM: not(n0()) -> n1() not(n1()) -> n0() and(x,n0()) -> n0() and(x,n1()) -> x or(x,n0()) -> x or(x,n1()) -> n1() |
1.92 |
TPTP_SWV262-2_theory |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 3 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 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
OutputEQUATIONS:
Completion of TPTP_SWV262-2_theory
c_Message_Oparts(c_union(vg,vh,tc_Message_Omsg())) = c_union(c_Message_Oparts(vg),c_Message_Oparts(vh),tc_Message_Omsg()) c_union(c_emptyset(),vy,ta) = vy c_union(c_insert(va,vb,ta),vc,ta) = c_insert(va,c_union(vb,vc,ta),ta) COMPLETE TRS: RULES: c_union(c_emptyset(),vy,ta) -> vy c_union(c_insert(va,vb,ta),vc,ta) -> c_insert(va,c_union(vb,vc,ta),ta) c_union(c_Message_Oparts(vg),c_Message_Oparts(vh),tc_Message_Omsg()) -> c_Message_Oparts(c_union(vg,vh,tc_Message_Omsg())) SUCCESS Search time: 0.01 seconds |
0.02
OutputCOMPLETE SYSTEM: c_union(c_emptyset(),vg,vh) -> vg 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_insert(vg,vh,ta),vy,ta) -> c_insert(vg,c_union(vh,vy,ta),ta) STATISTICS: General number of iterations: 4 number of nodes: 7 number of processes: 3 time for orient: 0.02 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 7 (yes: 7, timeouts: 0) time limit for check: 2.00 termination time: 0.02 Deduction critical pair criterion: all redundant CPs in total: 4 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000069 Two: 0.000000 COMPLETE SYSTEM: c_union(c_emptyset(),vg,vh) -> vg 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_insert(vg,vh,ta),vy,ta) -> c_insert(vg,c_union(vh,vy,ta),ta) |
∞ |
WS06_proofreduction |
10.20
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 9 equalities: 151 restarts: 1 time/cache: 0 time/set ops: 0.007 time/maxk: 8.98 time/normalization: 0.35 time/overlaps: 0.443 time/orientation constraints: 1.994 time/project: 0 time/sat: 2.902 time/update context: 0.161 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),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(x,CongrAnd2(y)),CongrAnd1(z)) → trans(trans(x,CongrAnd1(z)),CongrAnd2(y))trans(trans(CongrAnd1(x),CongrAnd2(y)),AndTrue2) → trans(trans(CongrAnd2(y),AndTrue2),x)trans(trans(CongrAnd1(x),CongrAnd2(y)),AndFalse2) → trans(CongrAnd2(y),AndFalse2)trans(trans(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(trans(x,CongrAnd1(y)),CongrAnd2(z)),AndTrue2) → trans(trans(trans(x,CongrAnd2(z)),AndTrue2),y)trans(trans(trans(x,CongrAnd1(y)),CongrAnd2(z)),AndFalse2) → trans(trans(x,CongrAnd2(z)),AndFalse2)trans(trans(trans(x,CongrOr2(y)),CongrOr1(z)),OrTrue1) → trans(trans(x,CongrOr1(z)),OrTrue1)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(CongrAnd2(x),CongrAnd1(y)) → trans(CongrAnd1(y),CongrAnd2(x))trans(trans(x,CongrAnd2(y)),AndFalse1) → trans(x,AndFalse1)trans(trans(x,CongrAnd1(y)),AndFalse2) → trans(x,AndFalse2)trans(trans(x,CongrOr2(y)),OrTrue1) → trans(x,OrTrue1)trans(trans(x,CongrOr1(y)),OrTrue2) → trans(x,OrTrue2)trans(trans(x,CongrNot(y)),CongrNot(z)) → trans(x,CongrNot(trans(y,z)))trans(refl,x) → x,trans(x,refl) → x,CongrOr1(refl) → reflCongrOr2(refl) → reflCongrAnd1(refl) → reflCongrAnd2(refl) → reflCongrNot(refl) → refl) |
⊥ |
40.97
OutputCOMPLETE SYSTEM: CongrOr1(refl()) -> refl() CongrOr2(refl()) -> refl() CongrAnd1(refl()) -> refl() CongrAnd2(refl()) -> refl() CongrNot(refl()) -> refl() trans(refl(),x) -> x trans(x,refl()) -> x trans(CongrOr1(x),OrTrue2()) -> OrTrue2() trans(CongrOr2(x),OrTrue1()) -> OrTrue1() trans(CongrAnd1(x),AndFalse2()) -> AndFalse2() trans(CongrAnd2(x),AndFalse1()) -> AndFalse1() trans(CongrOr2(x),OrFalse1()) -> trans(OrFalse1(),x) trans(CongrOr1(x),OrFalse2()) -> trans(OrFalse2(),x) trans(CongrAnd2(x),AndTrue1()) -> trans(AndTrue1(),x) trans(CongrAnd1(x),AndTrue2()) -> trans(AndTrue2(),x) trans(trans(x,y),z) -> trans(x,trans(y,z)) trans(CongrNot(x),CongrNot(y)) -> CongrNot(trans(x,y)) trans(CongrAnd2(y),trans(AndFalse1(),x)) -> trans(AndFalse1(),x) trans(CongrAnd1(y),trans(AndFalse2(),x)) -> trans(AndFalse2(),x) trans(CongrOr2(y),trans(OrTrue1(),x)) -> trans(OrTrue1(),x) trans(CongrOr1(y),trans(OrTrue2(),x)) -> trans(OrTrue2(),x) trans(CongrOr1(x),trans(OrFalse2(),y)) -> trans(OrFalse2(),trans(x,y)) trans(CongrOr2(x),trans(OrFalse1(),y)) -> trans(OrFalse1(),trans(x,y)) trans(CongrAnd1(x),trans(AndTrue2(),y)) -> trans(AndTrue2(),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),CongrAnd1(y)) -> CongrAnd1(trans(x,y)) trans(CongrAnd1(x),trans(CongrAnd1(y),z)) -> trans(CongrAnd1(trans(x,y)),z) trans(CongrAnd1(y),trans(CongrAnd2(x),z)) -> trans(CongrAnd2(x),trans(CongrAnd1(y),z)) trans(CongrAnd2(x),CongrAnd1(y)) -> trans(CongrAnd1(y),CongrAnd2(x)) trans(CongrAnd2(x),trans(CongrAnd1(y),AndTrue1())) -> trans(CongrAnd1(y),trans(AndTrue1(),x)) trans(CongrAnd2(x),trans(CongrAnd1(y),AndFalse1())) -> trans(CongrAnd1(y),AndFalse1()) trans(CongrAnd2(x),trans(CongrAnd1(y),CongrAnd2(z))) -> trans(CongrAnd1(y),CongrAnd2(trans(x,z))) trans(CongrAnd2(x),CongrAnd2(y)) -> CongrAnd2(trans(x,y)) trans(CongrAnd2(x),trans(CongrAnd2(y),z)) -> trans(CongrAnd2(trans(x,y)),z) 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(CongrOr1(x),CongrOr1(y)) -> CongrOr1(trans(x,y)) trans(CongrOr1(x),trans(CongrOr1(y),z)) -> trans(CongrOr1(trans(x,y)),z) trans(CongrOr1(y),trans(CongrOr2(x),z)) -> trans(CongrOr2(x),trans(CongrOr1(y),z)) trans(CongrOr2(x),CongrOr1(y)) -> trans(CongrOr1(y),CongrOr2(x)) 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),CongrOr2(z))) -> trans(CongrOr1(y),CongrOr2(trans(x,z))) trans(CongrOr2(x),CongrOr2(y)) -> CongrOr2(trans(x,y)) trans(CongrOr2(x),trans(CongrOr2(y),z)) -> trans(CongrOr2(trans(x,y)),z) 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))) STATISTICS: General number of iterations: 91 number of nodes: 1682 number of processes: 30 time for orient: 37.35 time for rewrite: 0.34 time for deduce: 0.37 Isomorphism Check: renamings+ (detected automatically) time for checking: 0.799036 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.05 Process Killing killed 26 exceeding best by: 71% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 763 (yes: 476, timeouts: 0) time limit for check: 2.00 termination time: 36.99 Deduction critical pair criterion: all redundant CPs in total: 688 for successful process: 0 required time: 0.01 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.01 overlaps: 0.03 maintenance: 0.00 One: 0.027239 Two: 0.000000 COMPLETE SYSTEM: CongrOr1(refl()) -> refl() CongrOr2(refl()) -> refl() CongrAnd1(refl()) -> refl() CongrAnd2(refl()) -> refl() CongrNot(refl()) -> refl() trans(refl(),x) -> x trans(x,refl()) -> x trans(CongrOr1(x),OrTrue2()) -> OrTrue2() trans(CongrOr2(x),OrTrue1()) -> OrTrue1() trans(CongrAnd1(x),AndFalse2()) -> AndFalse2() trans(CongrAnd2(x),AndFalse1()) -> AndFalse1() trans(CongrOr2(x),OrFalse1()) -> trans(OrFalse1(),x) trans(CongrOr1(x),OrFalse2()) -> trans(OrFalse2(),x) trans(CongrAnd2(x),AndTrue1()) -> trans(AndTrue1(),x) trans(CongrAnd1(x),AndTrue2()) -> trans(AndTrue2(),x) trans(trans(x,y),z) -> trans(x,trans(y,z)) trans(CongrNot(x),CongrNot(y)) -> CongrNot(trans(x,y)) trans(CongrAnd2(y),trans(AndFalse1(),x)) -> trans(AndFalse1(),x) trans(CongrAnd1(y),trans(AndFalse2(),x)) -> trans(AndFalse2(),x) trans(CongrOr2(y),trans(OrTrue1(),x)) -> trans(OrTrue1(),x) trans(CongrOr1(y),trans(OrTrue2(),x)) -> trans(OrTrue2(),x) trans(CongrOr1(x),trans(OrFalse2(),y)) -> trans(OrFalse2(),trans(x,y)) trans(CongrOr2(x),trans(OrFalse1(),y)) -> trans(OrFalse1(),trans(x,y)) trans(CongrAnd1(x),trans(AndTrue2(),y)) -> trans(AndTrue2(),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),CongrAnd1(y)) -> CongrAnd1(trans(x,y)) trans(CongrAnd1(x),trans(CongrAnd1(y),z)) -> trans(CongrAnd1(trans(x,y)),z) trans(CongrAnd1(y),trans(CongrAnd2(x),z)) -> trans(CongrAnd2(x),trans(CongrAnd1(y),z)) trans(CongrAnd2(x),CongrAnd1(y)) -> trans(CongrAnd1(y),CongrAnd2(x)) trans(CongrAnd2(x),trans(CongrAnd1(y),AndTrue1())) -> trans(CongrAnd1(y),trans(AndTrue1(),x)) trans(CongrAnd2(x),trans(CongrAnd1(y),AndFalse1())) -> trans(CongrAnd1(y),AndFalse1()) trans(CongrAnd2(x),trans(CongrAnd1(y),CongrAnd2(z))) -> trans(CongrAnd1(y),CongrAnd2(trans(x,z))) trans(CongrAnd2(x),CongrAnd2(y)) -> CongrAnd2(trans(x,y)) trans(CongrAnd2(x),trans(CongrAnd2(y),z)) -> trans(CongrAnd2(trans(x,y)),z) 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(CongrOr1(x),CongrOr1(y)) -> CongrOr1(trans(x,y)) trans(CongrOr1(x),trans(CongrOr1(y),z)) -> trans(CongrOr1(trans(x,y)),z) trans(CongrOr1(y),trans(CongrOr2(x),z)) -> trans(CongrOr2(x),trans(CongrOr1(y),z)) trans(CongrOr2(x),CongrOr1(y)) -> trans(CongrOr1(y),CongrOr2(x)) 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),CongrOr2(z))) -> trans(CongrOr1(y),CongrOr2(trans(x,z))) trans(CongrOr2(x),CongrOr2(y)) -> CongrOr2(trans(x,y)) trans(CongrOr2(x),trans(CongrOr2(y),z)) -> trans(CongrOr2(trans(x,y)),z) 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))) |
∞ |
aufgabe3_2 |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 2 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))) |
0.00
OutputEQUATIONS:
Completion of aufgabe3_2
f(f(x)) = g(x) g(f(x)) = f(g(x)) COMPLETE TRS: RULES: f(f(x)) -> g(x) f(g(x)) -> g(f(x)) SUCCESS Search time: 0.00 seconds |
0.01
OutputCOMPLETE SYSTEM: g(x) -> f(f(x)) STATISTICS: General number of iterations: 2 number of nodes: 3 number of processes: 1 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.000003 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 2 (yes: 2, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 0 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000069 Two: 0.000000 COMPLETE SYSTEM: g(x) -> f(f(x)) |
1.88 |
aufgabe3_3 |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 5 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,) |
0.00
OutputEQUATIONS:
Completion of aufgabe3_3
f(f(f(x))) = x f(f(f(f(f(x))))) = x COMPLETE TRS: RULES: f(x) -> x SUCCESS Search time: 0.00 seconds |
0.01
OutputCOMPLETE SYSTEM: f(x) -> x STATISTICS: General number of iterations: 4 number of nodes: 4 number of processes: 0 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.000015 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 3 (yes: 3, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 0 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000068 Two: 0.000000 COMPLETE SYSTEM: f(x) -> x |
2.27 |
fggx |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 2 equalities: 5 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 fggx
(RULES g(g(g(x))) → x,f(x) → g(g(x))) |
0.00
OutputEQUATIONS:
Completion of fggx
f(g(x)) = x f(x) = g(g(x)) COMPLETE TRS: RULES: f(x) -> g(g(x)) g(g(g(x))) -> x SUCCESS Search time: 0.00 seconds |
0.02
OutputCOMPLETE SYSTEM: f(g(x)) -> x g(g(x)) -> f(x) f(f(x)) -> g(x) g(f(x)) -> x STATISTICS: General number of iterations: 5 number of nodes: 11 number of processes: 2 time for orient: 0.01 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: term permutations+ (detected automatically) time for checking: 0.000023 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 6 (yes: 6, timeouts: 0) time limit for check: 2.00 termination time: 0.01 Deduction critical pair criterion: all redundant CPs in total: 3 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000087 Two: 0.000000 COMPLETE SYSTEM: f(g(x)) -> x g(g(x)) -> f(x) f(f(x)) -> g(x) g(f(x)) -> x |
2.34 |
fib |
4.68
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 9 equalities: 146 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 4.288 time/normalization: 0.187 time/overlaps: 0.116 time/orientation constraints: 0.055 time/project: 0 time/sat: 0.046 time/update context: 0.137 Convergent TRS(VAR x y)
Completion of fib
(RULES p(x,y) → u(b(x,y))f(s(s(x))) → u(b(f(s(x)),f(x)))u(b(x,0)) → x,u(b(x,s(y))) → s(u(b(x,y)))n(b(x,y)) → b(u(b(x,y)),x)f(0) → 0f(s(0)) → s(0)g(x) → b(f(s(x)),f(x))) |
2.04
OutputEQUATIONS:
Completion of fib
p(x,0()) = x p(x,s(y)) = s(p(x,y)) f(0()) = 0() f(s(0())) = s(0()) f(s(s(z))) = p(f(s(z)),f(z)) g(0()) = b(s(0()),0()) g(s(z)) = n(g(z)) n(b(x,y)) = b(p(x,y),x) u(b(x,y)) = p(x,y) g(x) = b(f(s(x)),f(x)) COMPLETE TRS: RULES: f(0()) -> 0() f(s(0())) -> s(0()) g(x) -> b(f(s(x)),f(x)) u(b(x,s(y))) -> s(u(b(x,y))) n(b(x,y)) -> b(u(b(x,y)),x) p(x,y) -> u(b(x,y)) u(b(x,0())) -> x f(s(s(x))) -> u(b(f(s(x)),f(x))) SUCCESS Search time: 2.04 seconds |
0.74
OutputCOMPLETE SYSTEM: f(0()) -> 0() p(x,0()) -> x f(s(0())) -> s(0()) p(x,s(y)) -> s(p(x,y)) u(b(x,y)) -> p(x,y) n(b(x,y)) -> b(p(x,y),x) g(x) -> b(f(s(x)),f(x)) f(s(s(x))) -> p(f(s(x)),f(x)) STATISTICS: General number of iterations: 13 number of nodes: 124 number of processes: 49 time for orient: 0.63 time for rewrite: 0.02 time for deduce: 0.03 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 12 exceeding best by: 71% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 157 (yes: 140, timeouts: 0) time limit for check: 2.00 termination time: 0.62 Deduction critical pair criterion: all redundant CPs in total: 30 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.001580 Two: 0.000000 COMPLETE SYSTEM: f(0()) -> 0() p(x,0()) -> x f(s(0())) -> s(0()) p(x,s(y)) -> s(p(x,y)) u(b(x,y)) -> p(x,y) n(b(x,y)) -> b(p(x,y),x) g(x) -> b(f(s(x)),f(x)) f(s(s(x))) -> p(f(s(x)),f(x)) |
3.18 |
kb_fail | ∞ | ⊥ | ⊥ | ⊥ |
kb_fail1 | ∞ | ⊥ | ⊥ | ⊥ |
lr_theory |
0.96
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 6 equalities: 59 restarts: 0 time/cache: 0 time/set ops: 0.006 time/maxk: 0.69 time/normalization: 0.121 time/overlaps: 0.08 time/orientation constraints: 0.008 time/project: 0 time/sat: 0.023 time/update context: 0.026 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,) |
0.03
OutputEQUATIONS:
Completion of lr_theory
f(x,f(y,z)) = f(f(x,y),z) f(x,i(x)) = e() f(e(),x) = x COMPLETE TRS: RULES: f(x,i(x)) -> e() f(e(),x) -> x f(i(x),f(x,y)) -> y f(i(x),e()) -> i(x) i(f(x,y)) -> f(i(y),i(x)) f(f(x,y),z) -> f(x,f(y,z)) i(e()) -> e() f(y,f(i(y),x)) -> x i(i(x)) -> f(x,e()) SUCCESS Search time: 0.03 seconds |
0.87
OutputCOMPLETE SYSTEM: f(e(),x) -> x f(x,i(x)) -> e() i(e()) -> e() f(f(x,y),z) -> f(x,f(y,z)) f(x,f(i(x),y)) -> y f(x,e()) -> i(i(x)) f(i(i(x)),y) -> f(x,y) f(i(x),f(x,y)) -> y i(i(i(x))) -> i(x) i(f(x,y)) -> f(i(y),i(x)) STATISTICS: General number of iterations: 37 number of nodes: 659 number of processes: 8 time for orient: 0.49 time for rewrite: 0.07 time for deduce: 0.16 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.01 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 92 (yes: 80, timeouts: 0) time limit for check: 2.00 termination time: 0.48 Deduction critical pair criterion: all redundant CPs in total: 543 for successful process: 32 required time: 0.02 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.01 overlaps: 0.01 maintenance: 0.00 One: 0.001461 Two: 0.000000 COMPLETE SYSTEM: f(e(),x) -> x f(x,i(x)) -> e() i(e()) -> e() f(f(x,y),z) -> f(x,f(y,z)) f(x,f(i(x),y)) -> y f(x,e()) -> i(i(x)) f(i(i(x)),y) -> f(x,y) f(i(x),f(x,y)) -> y i(i(i(x))) -> i(x) i(f(x,y)) -> f(i(y),i(x)) |
4.82 |
rl_theory |
1.98
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 8 equalities: 80 restarts: 0 time/cache: 0 time/set ops: 0.007 time/maxk: 1.567 time/normalization: 0.239 time/overlaps: 0.099 time/orientation constraints: 0.01 time/project: 0 time/sat: 0.027 time/update context: 0.052 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,) |
0.07
OutputEQUATIONS:
Completion of rl_theory
f(x,f(y,z)) = f(f(x,y),z) f(i(x),x) = e() f(x,e()) = x COMPLETE TRS: RULES: f(i(x),x) -> e() f(x,e()) -> x i(i(x)) -> f(e(),x) f(f(x,y),z) -> f(x,f(y,z)) i(e()) -> e() f(x,f(e(),y)) -> f(x,y) f(i(y),f(y,x)) -> f(e(),x) f(x,f(y,i(y))) -> x i(f(y,x)) -> f(i(x),i(y)) f(e(),i(x)) -> i(x) f(e(),f(i(x),y)) -> f(i(x),y) f(x,f(z,f(i(z),y))) -> f(x,y) SUCCESS Search time: 0.07 seconds |
⊥ | 8.82 |
slothrop_ackermann |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 3 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))) |
0.00
OutputEQUATIONS:
Completion of slothrop_ackermann
a(z(),x) = s(x) a(s(x),z()) = a(x,s(z())) a(s(x),s(y)) = a(x,a(s(x),y)) COMPLETE TRS: 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)) SUCCESS Search time: 0.00 seconds |
0.03
OutputCOMPLETE SYSTEM: a(z(),x) -> s(x) a(s(x),z()) -> a(x,s(z())) a(s(x),s(y)) -> a(x,a(s(x),y)) STATISTICS: General number of iterations: 4 number of nodes: 14 number of processes: 4 time for orient: 0.01 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 8 (yes: 8, timeouts: 0) time limit for check: 2.00 termination time: 0.01 Deduction critical pair criterion: all redundant CPs in total: 6 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000071 Two: 0.000000 COMPLETE SYSTEM: a(z(),x) -> s(x) a(s(x),z()) -> a(x,s(z())) a(s(x),s(y)) -> a(x,a(s(x),y)) |
2.53 |
slothrop_cge |
5.81
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 8 equalities: 93 restarts: 1 time/cache: 0 time/set ops: 0.014 time/maxk: 5.271 time/normalization: 0.243 time/overlaps: 0.149 time/orientation constraints: 0.501 time/project: 0 time/sat: 2.515 time/update context: 0.059 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))) |
∞ |
5.73
OutputCOMPLETE SYSTEM: trans(refl(),x) -> x trans(symm(x),x) -> refl() trans(trans(x,y),z) -> trans(x,trans(y,z)) trans(f(x),f(y)) -> f(trans(x,y)) trans(g(x),g(y)) -> g(trans(x,y)) trans(f(y),g(x)) -> trans(g(x),f(y)) trans(symm(x),trans(x,y)) -> y trans(x,refl()) -> x symm(refl()) -> refl() symm(symm(x)) -> x trans(x,symm(x)) -> refl() trans(x,trans(symm(x),y)) -> y trans(f(x),trans(f(y),z)) -> trans(f(trans(x,y)),z) trans(f(y),trans(g(x),z)) -> trans(g(x),trans(f(y),z)) f(refl()) -> refl() symm(f(x)) -> f(symm(x)) symm(trans(x,y)) -> trans(symm(y),symm(x)) g(refl()) -> refl() trans(g(x),trans(g(y),z)) -> trans(g(trans(x,y)),z) symm(g(x)) -> g(symm(x)) STATISTICS: General number of iterations: 73 number of nodes: 2478 number of processes: 14 time for orient: 3.31 time for rewrite: 0.33 time for deduce: 0.45 Isomorphism Check: renamings+ (detected automatically) time for checking: 0.317005 Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.04 Process Killing killed 6 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 379 (yes: 290, timeouts: 0) time limit for check: 2.00 termination time: 3.18 Deduction critical pair criterion: all redundant CPs in total: 1143 for successful process: 19 required time: 0.03 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.01 encompassments: 0.02 overlaps: 0.02 maintenance: 0.00 One: 0.014506 Two: 0.000000 COMPLETE SYSTEM: trans(refl(),x) -> x trans(symm(x),x) -> refl() trans(trans(x,y),z) -> trans(x,trans(y,z)) trans(f(x),f(y)) -> f(trans(x,y)) trans(g(x),g(y)) -> g(trans(x,y)) trans(f(y),g(x)) -> trans(g(x),f(y)) trans(symm(x),trans(x,y)) -> y trans(x,refl()) -> x symm(refl()) -> refl() symm(symm(x)) -> x trans(x,symm(x)) -> refl() trans(x,trans(symm(x),y)) -> y trans(f(x),trans(f(y),z)) -> trans(f(trans(x,y)),z) trans(f(y),trans(g(x),z)) -> trans(g(x),trans(f(y),z)) f(refl()) -> refl() symm(f(x)) -> f(symm(x)) symm(trans(x,y)) -> trans(symm(y),symm(x)) g(refl()) -> refl() trans(g(x),trans(g(y),z)) -> trans(g(trans(x,y)),z) symm(g(x)) -> g(symm(x)) |
∞ |
slothrop_cge3 |
22.22
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 10 equalities: 113 restarts: 1 time/cache: 0 time/set ops: 0.028 time/maxk: 21.09 time/normalization: 0.389 time/overlaps: 0.417 time/orientation constraints: 0.74 time/project: 0 time/sat: 15.73 time/update context: 0.121 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))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(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))) |
∞ | ⊥ | ∞ |
slothrop_endo |
2.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 7 equalities: 76 restarts: 0 time/cache: 0 time/set ops: 0.009 time/maxk: 1.567 time/normalization: 0.218 time/overlaps: 0.101 time/orientation constraints: 0.007 time/project: 0 time/sat: 0.048 time/update context: 0.061 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))) |
0.33
OutputEQUATIONS:
Completion of slothrop_endo
f(x,f(y,z)) = f(f(x,y),z) f(x,i(x)) = e() f(x,e()) = x h(f(x,y)) = f(h(x),h(y)) COMPLETE TRS: RULES: f(x,i(x)) -> e() f(x,e()) -> x h(f(x,y)) -> f(h(x),h(y)) h(e()) -> e() f(e(),x) -> x f(i(x),x) -> e() f(i(x),f(x,y)) -> y f(f(x,y),z) -> f(x,f(y,z)) f(y,f(i(y),x)) -> x i(e()) -> e() i(i(x)) -> x i(f(y,x)) -> f(i(x),i(y)) h(i(x)) -> i(h(x)) SUCCESS Search time: 0.33 seconds |
0.89
OutputCOMPLETE SYSTEM: f(x,e()) -> x f(x,i(x)) -> e() f(x,f(y,z)) -> f(f(x,y),z) f(h(x),h(y)) -> h(f(x,y)) f(f(x,y),i(y)) -> x f(e(),x) -> x i(e()) -> e() i(i(x)) -> x f(i(x),x) -> e() f(f(x,i(y)),y) -> x f(f(x,h(y)),h(z)) -> f(x,h(f(y,z))) h(e()) -> e() i(h(x)) -> h(i(x)) i(f(x,y)) -> f(i(y),i(x)) STATISTICS: General number of iterations: 30 number of nodes: 638 number of processes: 13 time for orient: 0.61 time for rewrite: 0.07 time for deduce: 0.09 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.01 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 116 (yes: 105, timeouts: 0) time limit for check: 2.00 termination time: 0.60 Deduction critical pair criterion: all redundant CPs in total: 314 for successful process: 14 required time: 0.01 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.001068 Two: 0.000000 COMPLETE SYSTEM: f(x,e()) -> x f(x,i(x)) -> e() f(x,f(y,z)) -> f(f(x,y),z) f(h(x),h(y)) -> h(f(x,y)) f(f(x,y),i(y)) -> x f(e(),x) -> x i(e()) -> e() i(i(x)) -> x f(i(x),x) -> e() f(f(x,i(y)),y) -> x f(f(x,h(y)),h(z)) -> f(x,h(f(y,z))) h(e()) -> e() i(h(x)) -> h(i(x)) i(f(x,y)) -> f(i(y),i(x)) |
∞ |
slothrop_equiv_proofs |
2.73
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 6 equalities: 90 restarts: 1 time/cache: 0 time/set ops: 0.002 time/maxk: 2.418 time/normalization: 0.081 time/overlaps: 0.106 time/orientation constraints: 1.029 time/project: 0 time/sat: 0.329 time/update context: 0.035 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) |
⊥ |
1.42
OutputCOMPLETE SYSTEM: congror1(refl()) -> refl() congror2(refl()) -> refl() trans(refl(),x1) -> x1 trans(x1,refl()) -> x1 trans(ortrue1(),x1) -> ortrue1() trans(ortrue2(),x1) -> ortrue2() trans(congror1(x1),ortrue2()) -> ortrue2() trans(congror2(x1),ortrue1()) -> ortrue1() trans(congror2(x1),orfalse1()) -> trans(orfalse1(),x1) trans(congror1(x1),orfalse2()) -> trans(orfalse2(),x1) trans(trans(x1,x2),x3) -> trans(x1,trans(x2,x3)) trans(congror1(x1),trans(orfalse2(),x2)) -> trans(orfalse2(),trans(x1,x2)) trans(congror2(x1),trans(orfalse1(),x2)) -> trans(orfalse1(),trans(x1,x2)) trans(congror2(x1),congror1(x2)) -> trans(congror1(x2),congror2(x1)) trans(congror1(x1),congror1(x2)) -> congror1(trans(x1,x2)) trans(congror1(x2),trans(congror2(x1),x3)) -> trans(congror2(x1),trans(congror1(x2),x3)) trans(congror1(x1),trans(congror1(x2),x3)) -> trans(congror1(trans(x1,x2)),x3) trans(congror2(x1),trans(congror1(x2),orfalse1())) -> trans(congror1(x2),trans(orfalse1(),x1)) trans(congror2(x1),trans(congror1(x2),ortrue1())) -> trans(congror1(x2),ortrue1()) trans(congror2(x1),trans(congror1(x2),congror2(x3))) -> trans(congror1(x2),congror2(trans(x1,x3))) trans(congror2(x1),congror2(x2)) -> congror2(trans(x1,x2)) trans(congror2(x1),trans(congror2(x2),x3)) -> trans(congror2(trans(x1,x2)),x3) trans(congror2(x1),trans(congror1(x2),trans(orfalse1(),x3))) -> trans(congror1(x2),trans(orfalse1(),trans(x1,x3))) STATISTICS: General number of iterations: 37 number of nodes: 513 number of processes: 5 time for orient: 1.15 time for rewrite: 0.06 time for deduce: 0.06 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.01 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 96 (yes: 60, timeouts: 0) time limit for check: 2.00 termination time: 1.13 Deduction critical pair criterion: all redundant CPs in total: 214 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.001848 Two: 0.000000 COMPLETE SYSTEM: congror1(refl()) -> refl() congror2(refl()) -> refl() trans(refl(),x1) -> x1 trans(x1,refl()) -> x1 trans(ortrue1(),x1) -> ortrue1() trans(ortrue2(),x1) -> ortrue2() trans(congror1(x1),ortrue2()) -> ortrue2() trans(congror2(x1),ortrue1()) -> ortrue1() trans(congror2(x1),orfalse1()) -> trans(orfalse1(),x1) trans(congror1(x1),orfalse2()) -> trans(orfalse2(),x1) trans(trans(x1,x2),x3) -> trans(x1,trans(x2,x3)) trans(congror1(x1),trans(orfalse2(),x2)) -> trans(orfalse2(),trans(x1,x2)) trans(congror2(x1),trans(orfalse1(),x2)) -> trans(orfalse1(),trans(x1,x2)) trans(congror2(x1),congror1(x2)) -> trans(congror1(x2),congror2(x1)) trans(congror1(x1),congror1(x2)) -> congror1(trans(x1,x2)) trans(congror1(x2),trans(congror2(x1),x3)) -> trans(congror2(x1),trans(congror1(x2),x3)) trans(congror1(x1),trans(congror1(x2),x3)) -> trans(congror1(trans(x1,x2)),x3) trans(congror2(x1),trans(congror1(x2),orfalse1())) -> trans(congror1(x2),trans(orfalse1(),x1)) trans(congror2(x1),trans(congror1(x2),ortrue1())) -> trans(congror1(x2),ortrue1()) trans(congror2(x1),trans(congror1(x2),congror2(x3))) -> trans(congror1(x2),congror2(trans(x1,x3))) trans(congror2(x1),congror2(x2)) -> congror2(trans(x1,x2)) trans(congror2(x1),trans(congror2(x2),x3)) -> trans(congror2(trans(x1,x2)),x3) trans(congror2(x1),trans(congror1(x2),trans(orfalse1(),x3))) -> trans(congror1(x2),trans(orfalse1(),trans(x1,x3))) |
⊥ |
slothrop_equiv_proofs_or |
2.19
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 6 equalities: 90 restarts: 1 time/cache: 0 time/set ops: 0.002 time/maxk: 1.927 time/normalization: 0.067 time/overlaps: 0.082 time/orientation constraints: 0.824 time/project: 0 time/sat: 0.278 time/update context: 0.027 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) |
⊥ |
1.43
OutputCOMPLETE SYSTEM: congror1(refl()) -> refl() congror2(refl()) -> refl() trans(refl(),x) -> x trans(x,refl()) -> x trans(ortrue1(),x) -> ortrue1() trans(ortrue2(),x) -> ortrue2() trans(congror1(x),ortrue2()) -> ortrue2() trans(congror2(x),ortrue1()) -> ortrue1() trans(congror2(x),orfalse1()) -> trans(orfalse1(),x) trans(congror1(x),orfalse2()) -> trans(orfalse2(),x) trans(trans(x,y),z) -> trans(x,trans(y,z)) trans(congror1(x),trans(orfalse2(),y)) -> trans(orfalse2(),trans(x,y)) trans(congror2(x),trans(orfalse1(),y)) -> trans(orfalse1(),trans(x,y)) trans(congror2(x),congror1(y)) -> trans(congror1(y),congror2(x)) trans(congror1(x),congror1(y)) -> congror1(trans(x,y)) trans(congror1(y),trans(congror2(x),z)) -> trans(congror2(x),trans(congror1(y),z)) trans(congror1(x),trans(congror1(y),z)) -> trans(congror1(trans(x,y)),z) trans(congror2(x),trans(congror1(y),orfalse1())) -> trans(congror1(y),trans(orfalse1(),x)) trans(congror2(x),trans(congror1(y),ortrue1())) -> trans(congror1(y),ortrue1()) trans(congror2(x),trans(congror1(y),congror2(z))) -> trans(congror1(y),congror2(trans(x,z))) trans(congror2(x),congror2(y)) -> congror2(trans(x,y)) trans(congror2(x),trans(congror2(y),z)) -> trans(congror2(trans(x,y)),z) trans(congror2(x),trans(congror1(y),trans(orfalse1(),z))) -> trans(congror1(y),trans(orfalse1(),trans(x,z))) STATISTICS: General number of iterations: 37 number of nodes: 513 number of processes: 5 time for orient: 1.17 time for rewrite: 0.06 time for deduce: 0.06 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 96 (yes: 60, timeouts: 0) time limit for check: 2.00 termination time: 1.15 Deduction critical pair criterion: all redundant CPs in total: 214 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000855 Two: 0.000000 COMPLETE SYSTEM: congror1(refl()) -> refl() congror2(refl()) -> refl() trans(refl(),x) -> x trans(x,refl()) -> x trans(ortrue1(),x) -> ortrue1() trans(ortrue2(),x) -> ortrue2() trans(congror1(x),ortrue2()) -> ortrue2() trans(congror2(x),ortrue1()) -> ortrue1() trans(congror2(x),orfalse1()) -> trans(orfalse1(),x) trans(congror1(x),orfalse2()) -> trans(orfalse2(),x) trans(trans(x,y),z) -> trans(x,trans(y,z)) trans(congror1(x),trans(orfalse2(),y)) -> trans(orfalse2(),trans(x,y)) trans(congror2(x),trans(orfalse1(),y)) -> trans(orfalse1(),trans(x,y)) trans(congror2(x),congror1(y)) -> trans(congror1(y),congror2(x)) trans(congror1(x),congror1(y)) -> congror1(trans(x,y)) trans(congror1(y),trans(congror2(x),z)) -> trans(congror2(x),trans(congror1(y),z)) trans(congror1(x),trans(congror1(y),z)) -> trans(congror1(trans(x,y)),z) trans(congror2(x),trans(congror1(y),orfalse1())) -> trans(congror1(y),trans(orfalse1(),x)) trans(congror2(x),trans(congror1(y),ortrue1())) -> trans(congror1(y),ortrue1()) trans(congror2(x),trans(congror1(y),congror2(z))) -> trans(congror1(y),congror2(trans(x,z))) trans(congror2(x),congror2(y)) -> congror2(trans(x,y)) trans(congror2(x),trans(congror2(y),z)) -> trans(congror2(trans(x,y)),z) trans(congror2(x),trans(congror1(y),trans(orfalse1(),z))) -> trans(congror1(y),trans(orfalse1(),trans(x,z))) |
⊥ |
slothrop_fgh |
0.01
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 3 equalities: 7 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 y)
Completion of slothrop_fgh
(RULES g(x,y) → af(x) → ah(x,y) → a) |
0.01
OutputEQUATIONS:
Completion of slothrop_fgh
h(x,y) = f(x) h(x,y) = f(y) g(x,y) = h(x,y) g(x,y) = a() COMPLETE TRS: RULES: h(x,y) -> a() g(x,y) -> a() f(x) -> a() SUCCESS Search time: 0.01 seconds |
0.01
OutputCOMPLETE SYSTEM: g(x,y) -> a() f(x) -> a() h(x,y) -> a() STATISTICS: General number of iterations: 6 number of nodes: 8 number of processes: 0 time for orient: 0.00 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 3 (yes: 3, timeouts: 0) time limit for check: 2.00 termination time: 0.00 Deduction critical pair criterion: all redundant CPs in total: 0 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000113 Two: 0.000000 COMPLETE SYSTEM: g(x,y) -> a() f(x) -> a() h(x,y) -> a() |
2.37 |
slothrop_groups |
1.05
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 7 equalities: 63 restarts: 0 time/cache: 0 time/set ops: 0.004 time/maxk: 0.846 time/normalization: 0.1 time/overlaps: 0.059 time/orientation constraints: 0.005 time/project: 0 time/sat: 0.025 time/update context: 0.026 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,) |
0.04
OutputEQUATIONS:
Completion of slothrop_groups
f(x,f(y,z)) = f(f(x,y),z) f(x,i(x)) = e() f(x,e()) = x COMPLETE TRS: RULES: f(x,i(x)) -> e() f(x,e()) -> x f(e(),x) -> x f(i(x),x) -> e() f(i(x),f(x,y)) -> y f(f(x,y),z) -> f(x,f(y,z)) f(y,f(i(y),x)) -> x i(e()) -> e() i(i(x)) -> x i(f(y,x)) -> f(i(x),i(y)) SUCCESS Search time: 0.04 seconds |
0.21
OutputCOMPLETE SYSTEM: f(x,e()) -> x f(x,i(x)) -> e() f(x,f(y,z)) -> f(f(x,y),z) f(f(x,y),i(y)) -> x f(e(),x) -> x i(e()) -> e() i(i(x)) -> x f(i(x),x) -> e() f(f(x,i(y)),y) -> x i(f(x,y)) -> f(i(y),i(x)) STATISTICS: General number of iterations: 21 number of nodes: 224 number of processes: 3 time for orient: 0.14 time for rewrite: 0.02 time for deduce: 0.03 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 35 (yes: 32, timeouts: 0) time limit for check: 2.00 termination time: 0.13 Deduction critical pair criterion: all redundant CPs in total: 153 for successful process: 11 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000345 Two: 0.000000 COMPLETE SYSTEM: f(x,e()) -> x f(x,i(x)) -> e() f(x,f(y,z)) -> f(f(x,y),z) f(f(x,y),i(y)) -> x f(e(),x) -> x i(e()) -> e() i(i(x)) -> x f(i(x),x) -> e() f(f(x,i(y)),y) -> x i(f(x,y)) -> f(i(y),i(x)) |
5.10 |
slothrop_groups_conj |
0.03
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 4 equalities: 17 restarts: 0 time/cache: 0 time/set ops: 0 time/maxk: 0.019 time/normalization: 0.003 time/overlaps: 0.003 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))) |
0.01
OutputEQUATIONS:
Completion of slothrop_groups_conj
f(x,f(y,z)) = f(f(x,y),z) f(x,i(x)) = e() f(x,e()) = x f(e(),x) = x i(f(y,x)) = f(i(x),i(y)) COMPLETE TRS: RULES: f(x,i(x)) -> e() f(x,e()) -> x f(e(),x) -> x i(f(y,x)) -> f(i(x),i(y)) f(i(x),x) -> e() f(i(x),f(x,y)) -> y f(f(x,y),z) -> f(x,f(y,z)) i(e()) -> e() f(y,f(i(y),x)) -> x i(i(x)) -> x SUCCESS Search time: 0.01 seconds |
0.13
OutputCOMPLETE SYSTEM: f(x,e()) -> x f(e(),x) -> x f(x,i(x)) -> e() i(e()) -> e() f(x,f(y,z)) -> f(f(x,y),z) i(f(x,y)) -> f(i(y),i(x)) f(f(x,y),i(y)) -> x i(i(x)) -> x f(i(x),x) -> e() f(f(x,i(y)),y) -> x STATISTICS: General number of iterations: 13 number of nodes: 118 number of processes: 3 time for orient: 0.08 time for rewrite: 0.01 time for deduce: 0.02 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 25 (yes: 25, timeouts: 0) time limit for check: 2.00 termination time: 0.08 Deduction critical pair criterion: all redundant CPs in total: 78 for successful process: 9 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000344 Two: 0.000000 COMPLETE SYSTEM: f(x,e()) -> x f(e(),x) -> x f(x,i(x)) -> e() i(e()) -> e() f(x,f(y,z)) -> f(f(x,y),z) i(f(x,y)) -> f(i(y),i(x)) f(f(x,y),i(y)) -> x i(i(x)) -> x f(i(x),x) -> e() f(f(x,i(y)),y) -> x |
3.57 |
slothrop_hard |
0.00
Statisticsstrategy: [(Orders ([LPO]), [Red, Comp], [CPRed]), (Dp ([cfsn, LPO]), [Red, Comp], [CPRed]), (Orders ([LPO]), [Comp], [MaxRed])] k: if i < 3 then 6 else 2 n: 12 iterations: 1 equalities: 2 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,) |
0.00
OutputEQUATIONS:
Completion of slothrop_hard
plus(x,z()) = x s(plus(x,y)) = plus(x,s(y)) COMPLETE TRS: RULES: plus(x,z()) -> x plus(x,s(y)) -> s(plus(x,y)) SUCCESS Search time: 0.00 seconds |
0.01
OutputCOMPLETE SYSTEM: plus(x,z()) -> x plus(x,s(y)) -> s(plus(x,y)) STATISTICS: General number of iterations: 3 number of nodes: 3 number of processes: 1 time for orient: 0.01 time for rewrite: 0.00 time for deduce: 0.00 Isomorphism Check: none (detected automatically) Selection strategy: (el(min(e(sum(smax)) + c(sum(smax)))), (data(smax), ( -el(#), ?))) time for selection: 0.00 Process Killing killed 0 exceeding best by: 401% required time: 0.00 Termination Checks (internal) strategy: dp;(odg?; sccs?; (sc | csf | lpo | kbo -ib 2))* termination checks: 3 (yes: 3, timeouts: 0) time limit for check: 2.00 termination time: 0.01 Deduction critical pair criterion: all redundant CPs in total: 1 for successful process: 0 required time: 0.00 small lemmata propagation: 5 Indexing techniques: code tree (rewriting) discrimination tree (overlaps) variants: 0.00 encompassments: 0.00 overlaps: 0.00 maintenance: 0.00 One: 0.000065 Two: 0.000000 COMPLETE SYSTEM: plus(x,z()) -> x plus(x,s(y)) -> s(plus(x,y)) |
3.02 |
slothrop_nlp-2b | ∞ | ⊥ | ⊥ | ∞ |
successes | 97 | 87 | 85 | 88 |
avg. time | 17.421 | 1.224 | 4.802 | 15.761 |