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TRS Stand 20472 pair #381716405
details
property
value
status
complete
benchmark
PEANO_nokinds_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n085.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.558470010757 seconds
cpu usage
0.554892598
max memory
1.8092032E7
stage attributes
key
value
output-size
27862
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o U11 : [o * o] --> o U12 : [o] --> o U21 : [o] --> o U31 : [o * o] --> o U41 : [o * o * o] --> o U42 : [o * o * o] --> o a!6220!6220U11 : [o * o] --> o a!6220!6220U12 : [o] --> o a!6220!6220U21 : [o] --> o a!6220!6220U31 : [o * o] --> o a!6220!6220U41 : [o * o * o] --> o a!6220!6220U42 : [o * o * o] --> o a!6220!6220isNat : [o] --> o a!6220!6220plus : [o * o] --> o isNat : [o] --> o mark : [o] --> o plus : [o * o] --> o s : [o] --> o tt : [] --> o a!6220!6220U11(tt, X) => a!6220!6220U12(a!6220!6220isNat(X)) a!6220!6220U12(tt) => tt a!6220!6220U21(tt) => tt a!6220!6220U31(tt, X) => mark(X) a!6220!6220U41(tt, X, Y) => a!6220!6220U42(a!6220!6220isNat(Y), X, Y) a!6220!6220U42(tt, X, Y) => s(a!6220!6220plus(mark(Y), mark(X))) a!6220!6220isNat(0) => tt a!6220!6220isNat(plus(X, Y)) => a!6220!6220U11(a!6220!6220isNat(X), Y) a!6220!6220isNat(s(X)) => a!6220!6220U21(a!6220!6220isNat(X)) a!6220!6220plus(X, 0) => a!6220!6220U31(a!6220!6220isNat(X), X) a!6220!6220plus(X, s(Y)) => a!6220!6220U41(a!6220!6220isNat(Y), Y, X) mark(U11(X, Y)) => a!6220!6220U11(mark(X), Y) mark(U12(X)) => a!6220!6220U12(mark(X)) mark(isNat(X)) => a!6220!6220isNat(X) mark(U21(X)) => a!6220!6220U21(mark(X)) mark(U31(X, Y)) => a!6220!6220U31(mark(X), Y) mark(U41(X, Y, Z)) => a!6220!6220U41(mark(X), Y, Z) mark(U42(X, Y, Z)) => a!6220!6220U42(mark(X), Y, Z) mark(plus(X, Y)) => a!6220!6220plus(mark(X), mark(Y)) mark(tt) => tt mark(s(X)) => s(mark(X)) mark(0) => 0 a!6220!6220U11(X, Y) => U11(X, Y) a!6220!6220U12(X) => U12(X) a!6220!6220isNat(X) => isNat(X) a!6220!6220U21(X) => U21(X) a!6220!6220U31(X, Y) => U31(X, Y) a!6220!6220U41(X, Y, Z) => U41(X, Y, Z) a!6220!6220U42(X, Y, Z) => U42(X, Y, Z) a!6220!6220plus(X, Y) => plus(X, Y) We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs in [Kop12, Ch. 7.8]). We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative): Dependency Pairs P_0: 0] a!6220!6220U11#(tt, X) =#> a!6220!6220U12#(a!6220!6220isNat(X)) 1] a!6220!6220U11#(tt, X) =#> a!6220!6220isNat#(X) 2] a!6220!6220U31#(tt, X) =#> mark#(X) 3] a!6220!6220U41#(tt, X, Y) =#> a!6220!6220U42#(a!6220!6220isNat(Y), X, Y) 4] a!6220!6220U41#(tt, X, Y) =#> a!6220!6220isNat#(Y) 5] a!6220!6220U42#(tt, X, Y) =#> a!6220!6220plus#(mark(Y), mark(X)) 6] a!6220!6220U42#(tt, X, Y) =#> mark#(Y) 7] a!6220!6220U42#(tt, X, Y) =#> mark#(X) 8] a!6220!6220isNat#(plus(X, Y)) =#> a!6220!6220U11#(a!6220!6220isNat(X), Y) 9] a!6220!6220isNat#(plus(X, Y)) =#> a!6220!6220isNat#(X) 10] a!6220!6220isNat#(s(X)) =#> a!6220!6220U21#(a!6220!6220isNat(X)) 11] a!6220!6220isNat#(s(X)) =#> a!6220!6220isNat#(X) 12] a!6220!6220plus#(X, 0) =#> a!6220!6220U31#(a!6220!6220isNat(X), X) 13] a!6220!6220plus#(X, 0) =#> a!6220!6220isNat#(X) 14] a!6220!6220plus#(X, s(Y)) =#> a!6220!6220U41#(a!6220!6220isNat(Y), Y, X) 15] a!6220!6220plus#(X, s(Y)) =#> a!6220!6220isNat#(Y) 16] mark#(U11(X, Y)) =#> a!6220!6220U11#(mark(X), Y) 17] mark#(U11(X, Y)) =#> mark#(X) 18] mark#(U12(X)) =#> a!6220!6220U12#(mark(X)) 19] mark#(U12(X)) =#> mark#(X) 20] mark#(isNat(X)) =#> a!6220!6220isNat#(X) 21] mark#(U21(X)) =#> a!6220!6220U21#(mark(X)) 22] mark#(U21(X)) =#> mark#(X) 23] mark#(U31(X, Y)) =#> a!6220!6220U31#(mark(X), Y) 24] mark#(U31(X, Y)) =#> mark#(X) 25] mark#(U41(X, Y, Z)) =#> a!6220!6220U41#(mark(X), Y, Z) 26] mark#(U41(X, Y, Z)) =#> mark#(X) 27] mark#(U42(X, Y, Z)) =#> a!6220!6220U42#(mark(X), Y, Z) 28] mark#(U42(X, Y, Z)) =#> mark#(X) 29] mark#(plus(X, Y)) =#> a!6220!6220plus#(mark(X), mark(Y)) 30] mark#(plus(X, Y)) =#> mark#(X)
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