YES(O(1), O(1)) 68.05/30.82 YES(O(1), O(1)) 68.05/30.83 68.05/30.83 68.05/30.83
68.05/30.83 68.05/30.830 CpxTRS68.05/30.83
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))68.05/30.83
↳2 CdtProblem68.05/30.83
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))68.05/30.83
↳4 CdtProblem68.05/30.83
↳5 CdtNarrowingProof (BOTH BOUNDS(ID, ID))68.05/30.83
↳6 CdtProblem68.05/30.83
↳7 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))68.05/30.83
↳8 CdtProblem68.05/30.83
↳9 CdtNarrowingProof (BOTH BOUNDS(ID, ID))68.05/30.83
↳10 CdtProblem68.05/30.83
↳11 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))68.05/30.83
↳12 CdtProblem68.05/30.83
↳13 CdtRewritingProof (BOTH BOUNDS(ID, ID))68.05/30.83
↳14 CdtProblem68.05/30.83
↳15 CdtInstantiationProof (BOTH BOUNDS(ID, ID))68.05/30.83
↳16 CdtProblem68.05/30.83
↳17 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))68.05/30.83
↳18 CdtProblem68.05/30.83
↳19 CdtUnreachableProof (⇔)68.05/30.83
↳20 CdtProblem68.05/30.83
↳21 SIsEmptyProof (BOTH BOUNDS(ID, ID))68.05/30.83
↳22 BOUNDS(O(1), O(1))68.05/30.83
b(y, z) → f(c(c(y, z, z), a, a)) 68.05/30.83
b(b(z, y), a) → z 68.05/30.83
c(f(z), f(c(a, x, a)), y) → c(f(b(x, z)), c(z, y, a), a)
Tuples:
b(z0, z1) → f(c(c(z0, z1, z1), a, a)) 68.05/30.83
b(b(z0, z1), a) → z0 68.05/30.83
c(f(z0), f(c(a, z1, a)), z2) → c(f(b(z1, z0)), c(z0, z2, a), a)
S tuples:
B(z0, z1) → c1(C(c(z0, z1, z1), a, a), C(z0, z1, z1)) 68.05/30.83
C(f(z0), f(c(a, z1, a)), z2) → c3(C(f(b(z1, z0)), c(z0, z2, a), a), B(z1, z0), C(z0, z2, a))
K tuples:none
B(z0, z1) → c1(C(c(z0, z1, z1), a, a), C(z0, z1, z1)) 68.05/30.87
C(f(z0), f(c(a, z1, a)), z2) → c3(C(f(b(z1, z0)), c(z0, z2, a), a), B(z1, z0), C(z0, z2, a))
b, c
B, C
c1, c3
Tuples:
b(z0, z1) → f(c(c(z0, z1, z1), a, a)) 68.05/30.87
b(b(z0, z1), a) → z0 68.05/30.87
c(f(z0), f(c(a, z1, a)), z2) → c(f(b(z1, z0)), c(z0, z2, a), a)
S tuples:
C(f(z0), f(c(a, z1, a)), z2) → c3(C(f(b(z1, z0)), c(z0, z2, a), a), B(z1, z0), C(z0, z2, a)) 68.05/30.87
B(z0, z1) → c1(C(z0, z1, z1))
K tuples:none
C(f(z0), f(c(a, z1, a)), z2) → c3(C(f(b(z1, z0)), c(z0, z2, a), a), B(z1, z0), C(z0, z2, a)) 68.05/30.87
B(z0, z1) → c1(C(z0, z1, z1))
b, c
C, B
c3, c1
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(C(f(b(x1, f(z0))), c(f(b(z1, z0)), c(z0, a, a), a), a), B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(z1), f(c(a, z0, a)), x2) → c3(C(f(f(c(c(z0, z1, z1), a, a))), c(z1, x2, a), a), B(z0, z1), C(z1, x2, a))
Tuples:
b(z0, z1) → f(c(c(z0, z1, z1), a, a)) 68.05/30.87
b(b(z0, z1), a) → z0 68.05/30.87
c(f(z0), f(c(a, z1, a)), z2) → c(f(b(z1, z0)), c(z0, z2, a), a)
S tuples:
B(z0, z1) → c1(C(z0, z1, z1)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(C(f(b(x1, f(z0))), c(f(b(z1, z0)), c(z0, a, a), a), a), B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(z1), f(c(a, z0, a)), x2) → c3(C(f(f(c(c(z0, z1, z1), a, a))), c(z1, x2, a), a), B(z0, z1), C(z1, x2, a))
K tuples:none
B(z0, z1) → c1(C(z0, z1, z1)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(C(f(b(x1, f(z0))), c(f(b(z1, z0)), c(z0, a, a), a), a), B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(z1), f(c(a, z0, a)), x2) → c3(C(f(f(c(c(z0, z1, z1), a, a))), c(z1, x2, a), a), B(z0, z1), C(z1, x2, a))
b, c
B, C
c1, c3
Tuples:
b(z0, z1) → f(c(c(z0, z1, z1), a, a)) 68.05/30.87
b(b(z0, z1), a) → z0 68.05/30.87
c(f(z0), f(c(a, z1, a)), z2) → c(f(b(z1, z0)), c(z0, z2, a), a)
S tuples:
B(z0, z1) → c1(C(z0, z1, z1)) 68.05/30.87
C(f(z1), f(c(a, z0, a)), x2) → c3(C(f(f(c(c(z0, z1, z1), a, a))), c(z1, x2, a), a), B(z0, z1), C(z1, x2, a)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a))
K tuples:none
B(z0, z1) → c1(C(z0, z1, z1)) 68.05/30.87
C(f(z1), f(c(a, z0, a)), x2) → c3(C(f(f(c(c(z0, z1, z1), a, a))), c(z1, x2, a), a), B(z0, z1), C(z1, x2, a)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a))
b, c
B, C
c1, c3, c3
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(C(f(f(c(c(x1, f(z0), f(z0)), a, a))), c(f(b(z1, z0)), c(z0, a, a), a), a), B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(f(c(a, z1, a))), f(c(a, f(z0), a)), x2) → c3(C(f(f(c(c(f(b(z1, z0)), c(z0, f(c(a, z1, a)), a), a), a, a))), c(f(c(a, z1, a)), x2, a), a), B(f(z0), f(c(a, z1, a))), C(f(c(a, z1, a)), x2, a)) 68.05/30.87
C(f(x0), f(c(a, x1, a)), x2) → c3(B(x1, x0))
Tuples:
b(z0, z1) → f(c(c(z0, z1, z1), a, a)) 68.05/30.87
b(b(z0, z1), a) → z0 68.05/30.87
c(f(z0), f(c(a, z1, a)), z2) → c(f(b(z1, z0)), c(z0, z2, a), a)
S tuples:
B(z0, z1) → c1(C(z0, z1, z1)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(C(f(f(c(c(x1, f(z0), f(z0)), a, a))), c(f(b(z1, z0)), c(z0, a, a), a), a), B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(f(c(a, z1, a))), f(c(a, f(z0), a)), x2) → c3(C(f(f(c(c(f(b(z1, z0)), c(z0, f(c(a, z1, a)), a), a), a, a))), c(f(c(a, z1, a)), x2, a), a), B(f(z0), f(c(a, z1, a))), C(f(c(a, z1, a)), x2, a)) 68.05/30.87
C(f(x0), f(c(a, x1, a)), x2) → c3(B(x1, x0))
K tuples:none
B(z0, z1) → c1(C(z0, z1, z1)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(C(f(f(c(c(x1, f(z0), f(z0)), a, a))), c(f(b(z1, z0)), c(z0, a, a), a), a), B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(f(c(a, z1, a))), f(c(a, f(z0), a)), x2) → c3(C(f(f(c(c(f(b(z1, z0)), c(z0, f(c(a, z1, a)), a), a), a, a))), c(f(c(a, z1, a)), x2, a), a), B(f(z0), f(c(a, z1, a))), C(f(c(a, z1, a)), x2, a)) 68.05/30.87
C(f(x0), f(c(a, x1, a)), x2) → c3(B(x1, x0))
b, c
B, C
c1, c3, c3, c3
Tuples:
b(z0, z1) → f(c(c(z0, z1, z1), a, a)) 68.05/30.87
b(b(z0, z1), a) → z0 68.05/30.87
c(f(z0), f(c(a, z1, a)), z2) → c(f(b(z1, z0)), c(z0, z2, a), a)
S tuples:
B(z0, z1) → c1(C(z0, z1, z1)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(f(c(a, z1, a))), f(c(a, f(z0), a)), x2) → c3(C(f(f(c(c(f(b(z1, z0)), c(z0, f(c(a, z1, a)), a), a), a, a))), c(f(c(a, z1, a)), x2, a), a), B(f(z0), f(c(a, z1, a))), C(f(c(a, z1, a)), x2, a)) 68.05/30.87
C(f(x0), f(c(a, x1, a)), x2) → c3(B(x1, x0))
K tuples:none
B(z0, z1) → c1(C(z0, z1, z1)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(f(c(a, z1, a))), f(c(a, f(z0), a)), x2) → c3(C(f(f(c(c(f(b(z1, z0)), c(z0, f(c(a, z1, a)), a), a), a, a))), c(f(c(a, z1, a)), x2, a), a), B(f(z0), f(c(a, z1, a))), C(f(c(a, z1, a)), x2, a)) 68.05/30.87
C(f(x0), f(c(a, x1, a)), x2) → c3(B(x1, x0))
b, c
B, C
c1, c3, c3, c3
Tuples:
b(z0, z1) → f(c(c(z0, z1, z1), a, a)) 68.05/30.87
b(b(z0, z1), a) → z0 68.05/30.87
c(f(z0), f(c(a, z1, a)), z2) → c(f(b(z1, z0)), c(z0, z2, a), a)
S tuples:
B(z0, z1) → c1(C(z0, z1, z1)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(x0), f(c(a, x1, a)), x2) → c3(B(x1, x0)) 68.05/30.87
C(f(f(c(a, z0, a))), f(c(a, f(z1), a)), z2) → c3(C(f(f(c(c(f(f(c(c(z0, z1, z1), a, a))), c(z1, f(c(a, z0, a)), a), a), a, a))), c(f(c(a, z0, a)), z2, a), a), B(f(z1), f(c(a, z0, a))), C(f(c(a, z0, a)), z2, a))
K tuples:none
B(z0, z1) → c1(C(z0, z1, z1)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(x0), f(c(a, x1, a)), x2) → c3(B(x1, x0)) 68.05/30.87
C(f(f(c(a, z0, a))), f(c(a, f(z1), a)), z2) → c3(C(f(f(c(c(f(f(c(c(z0, z1, z1), a, a))), c(z1, f(c(a, z0, a)), a), a), a, a))), c(f(c(a, z0, a)), z2, a), a), B(f(z1), f(c(a, z0, a))), C(f(c(a, z0, a)), z2, a))
b, c
B, C
c1, c3, c3, c3
C(f(z0), f(c(a, z1, a)), f(c(a, z1, a))) → c3(B(z1, z0)) 68.05/30.87
C(f(x0), f(c(a, x2, a)), a) → c3(B(x2, x0)) 68.05/30.87
C(f(f(c(y2, a, a))), f(c(a, z1, a)), a) → c3(B(z1, f(c(y2, a, a)))) 68.05/30.87
C(f(c(a, x0, a)), f(c(a, z1, a)), a) → c3(B(z1, c(a, x0, a)))
Tuples:
b(z0, z1) → f(c(c(z0, z1, z1), a, a)) 68.05/30.87
b(b(z0, z1), a) → z0 68.05/30.87
c(f(z0), f(c(a, z1, a)), z2) → c(f(b(z1, z0)), c(z0, z2, a), a)
S tuples:
B(z0, z1) → c1(C(z0, z1, z1)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(f(c(a, z0, a))), f(c(a, f(z1), a)), z2) → c3(C(f(f(c(c(f(f(c(c(z0, z1, z1), a, a))), c(z1, f(c(a, z0, a)), a), a), a, a))), c(f(c(a, z0, a)), z2, a), a), B(f(z1), f(c(a, z0, a))), C(f(c(a, z0, a)), z2, a)) 68.05/30.87
C(f(z0), f(c(a, z1, a)), f(c(a, z1, a))) → c3(B(z1, z0)) 68.05/30.87
C(f(x0), f(c(a, x2, a)), a) → c3(B(x2, x0)) 68.05/30.87
C(f(f(c(y2, a, a))), f(c(a, z1, a)), a) → c3(B(z1, f(c(y2, a, a)))) 68.05/30.87
C(f(c(a, x0, a)), f(c(a, z1, a)), a) → c3(B(z1, c(a, x0, a)))
K tuples:none
B(z0, z1) → c1(C(z0, z1, z1)) 68.05/30.87
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(f(c(a, z0, a))), f(c(a, f(z1), a)), z2) → c3(C(f(f(c(c(f(f(c(c(z0, z1, z1), a, a))), c(z1, f(c(a, z0, a)), a), a), a, a))), c(f(c(a, z0, a)), z2, a), a), B(f(z1), f(c(a, z0, a))), C(f(c(a, z0, a)), z2, a)) 68.05/30.87
C(f(z0), f(c(a, z1, a)), f(c(a, z1, a))) → c3(B(z1, z0)) 68.05/30.87
C(f(x0), f(c(a, x2, a)), a) → c3(B(x2, x0)) 68.05/30.87
C(f(f(c(y2, a, a))), f(c(a, z1, a)), a) → c3(B(z1, f(c(y2, a, a)))) 68.05/30.87
C(f(c(a, x0, a)), f(c(a, z1, a)), a) → c3(B(z1, c(a, x0, a)))
b, c
B, C
c1, c3, c3, c3
B(f(f(y0)), f(c(a, y1, a))) → c1(C(f(f(y0)), f(c(a, y1, a)), f(c(a, y1, a)))) 68.05/30.87
B(f(f(c(a, y0, a))), f(c(a, f(y1), a))) → c1(C(f(f(c(a, y0, a))), f(c(a, f(y1), a)), f(c(a, f(y1), a)))) 68.05/30.87
B(f(y0), f(c(a, y1, a))) → c1(C(f(y0), f(c(a, y1, a)), f(c(a, y1, a))))
Tuples:
b(z0, z1) → f(c(c(z0, z1, z1), a, a)) 68.05/30.87
b(b(z0, z1), a) → z0 68.05/30.87
c(f(z0), f(c(a, z1, a)), z2) → c(f(b(z1, z0)), c(z0, z2, a), a)
S tuples:
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(f(c(a, z0, a))), f(c(a, f(z1), a)), z2) → c3(C(f(f(c(c(f(f(c(c(z0, z1, z1), a, a))), c(z1, f(c(a, z0, a)), a), a), a, a))), c(f(c(a, z0, a)), z2, a), a), B(f(z1), f(c(a, z0, a))), C(f(c(a, z0, a)), z2, a)) 68.05/30.87
C(f(z0), f(c(a, z1, a)), f(c(a, z1, a))) → c3(B(z1, z0)) 68.05/30.87
C(f(x0), f(c(a, x2, a)), a) → c3(B(x2, x0)) 68.05/30.87
C(f(f(c(y2, a, a))), f(c(a, z1, a)), a) → c3(B(z1, f(c(y2, a, a)))) 68.05/30.87
C(f(c(a, x0, a)), f(c(a, z1, a)), a) → c3(B(z1, c(a, x0, a))) 68.05/30.87
B(f(f(y0)), f(c(a, y1, a))) → c1(C(f(f(y0)), f(c(a, y1, a)), f(c(a, y1, a)))) 68.05/30.87
B(f(f(c(a, y0, a))), f(c(a, f(y1), a))) → c1(C(f(f(c(a, y0, a))), f(c(a, f(y1), a)), f(c(a, f(y1), a)))) 68.05/30.87
B(f(y0), f(c(a, y1, a))) → c1(C(f(y0), f(c(a, y1, a)), f(c(a, y1, a))))
K tuples:none
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(f(c(a, z0, a))), f(c(a, f(z1), a)), z2) → c3(C(f(f(c(c(f(f(c(c(z0, z1, z1), a, a))), c(z1, f(c(a, z0, a)), a), a), a, a))), c(f(c(a, z0, a)), z2, a), a), B(f(z1), f(c(a, z0, a))), C(f(c(a, z0, a)), z2, a)) 68.05/30.87
C(f(z0), f(c(a, z1, a)), f(c(a, z1, a))) → c3(B(z1, z0)) 68.05/30.87
C(f(x0), f(c(a, x2, a)), a) → c3(B(x2, x0)) 68.05/30.87
C(f(f(c(y2, a, a))), f(c(a, z1, a)), a) → c3(B(z1, f(c(y2, a, a)))) 68.05/30.87
C(f(c(a, x0, a)), f(c(a, z1, a)), a) → c3(B(z1, c(a, x0, a))) 68.05/30.87
B(f(f(y0)), f(c(a, y1, a))) → c1(C(f(f(y0)), f(c(a, y1, a)), f(c(a, y1, a)))) 68.05/30.87
B(f(f(c(a, y0, a))), f(c(a, f(y1), a))) → c1(C(f(f(c(a, y0, a))), f(c(a, f(y1), a)), f(c(a, f(y1), a)))) 68.05/30.87
B(f(y0), f(c(a, y1, a))) → c1(C(f(y0), f(c(a, y1, a)), f(c(a, y1, a))))
b, c
C, B
c3, c3, c3, c1
C(f(f(z0)), f(c(a, x1, a)), f(c(a, z1, a))) → c3(B(x1, f(z0)), C(f(z0), f(c(a, z1, a)), a)) 68.05/30.87
C(f(f(c(a, z0, a))), f(c(a, f(z1), a)), z2) → c3(C(f(f(c(c(f(f(c(c(z0, z1, z1), a, a))), c(z1, f(c(a, z0, a)), a), a), a, a))), c(f(c(a, z0, a)), z2, a), a), B(f(z1), f(c(a, z0, a))), C(f(c(a, z0, a)), z2, a)) 68.05/30.87
C(f(z0), f(c(a, z1, a)), f(c(a, z1, a))) → c3(B(z1, z0)) 68.05/30.87
C(f(x0), f(c(a, x2, a)), a) → c3(B(x2, x0)) 68.05/30.87
C(f(f(c(y2, a, a))), f(c(a, z1, a)), a) → c3(B(z1, f(c(y2, a, a)))) 68.05/30.87
C(f(c(a, x0, a)), f(c(a, z1, a)), a) → c3(B(z1, c(a, x0, a))) 68.05/30.87
B(f(f(y0)), f(c(a, y1, a))) → c1(C(f(f(y0)), f(c(a, y1, a)), f(c(a, y1, a)))) 68.05/30.87
B(f(f(c(a, y0, a))), f(c(a, f(y1), a))) → c1(C(f(f(c(a, y0, a))), f(c(a, f(y1), a)), f(c(a, f(y1), a)))) 68.05/30.87
B(f(y0), f(c(a, y1, a))) → c1(C(f(y0), f(c(a, y1, a)), f(c(a, y1, a))))
Tuples:none
b(z0, z1) → f(c(c(z0, z1, z1), a, a)) 68.05/30.87
b(b(z0, z1), a) → z0 68.05/30.87
c(f(z0), f(c(a, z1, a)), z2) → c(f(b(z1, z0)), c(z0, z2, a), a)
b, c